2.6 kg is the mass of nitrogen in the bottle. The nitrogen contained in the bottle cannot be treated as an ideal gas. It is non-ideal. The mass of the nitrogen in the bottle is 2.6 kg. It is stated that the nitrogen has a pressure of 42 atm.
At this pressure, the nitrogen atoms are relatively close together, and they will start to attract one another. As a result, the attractive forces between the nitrogen atoms cannot be ignored. Therefore, nitrogen is non-ideal at this pressure.
The mass of nitrogen can be calculated using the ideal gas law. However, since the nitrogen is non-ideal, we will use the van der Waals equation, which takes into account the attractive forces between the nitrogen atoms. The van der Waals equation is given as:
(P + a(n/V)²)(V - nb) = nRT Where: P is the pressure of the nitrogen a is a constant that depends on the properties of the gas n is the number of moles of gas V is the volume of the gas b is a constant that depends on the properties of the gas R is the ideal gas constant, T is the temperature of the gas
Rearranging the equation and solving for n, we have: n = PV/RT + (nb/V) - a(n/V)²
Using the given values: P = 42 atm, V = 0.02 m³ T
= -143 + 273
= 130 Kas well as the constants for nitrogen: a = 1.39 b
= 0.03913
We can solve for n: n = 2.108 mol
The mass of nitrogen can be calculated using the formula: mass = n × M where M is the molar mass of nitrogen, which is 28 g/mol.
Therefore, the mass of nitrogen is: mass = 2.108 × 28
= 58.9 g
Converting to kg: 58.9/1000 = 0.0589 kg
Rounding off to two significant figures: 2.6 kg is the mass of nitrogen in the bottle.
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A man pushes a block of mass 20 kg so that it slides at constant velocity up a ramp that is inclined at 11o. Calculate the magnitude of the force parallel to the incline applied by the man if a) the incline is frictionless; b) the coefficient of kinetic friction between the block and incline is 0.25. (Draw its diagram before solving.)
Diagram of the block sliding up the inclined plane So, the magnitude of the force parallel to the incline applied by the man if the incline is frictionless is:
`F = mgsinθ Where m = 20 kg, θ = 11°
and g = 9.8 m/s².
[tex]F = 20 × 9.8 × sin 11°F ≈ 35.6 N[/tex]
Thus, the magnitude of the force parallel to the incline applied by the man if the incline is frictionless is 35.6 N.If the coefficient of kinetic friction between the block and incline is 0.25.
F_friction = μ_k N Where μ_k = 0.25 and `N = mg cos θ
Now, substituting the given values in the above formula, we get:
[tex]N = 20 × 9.8 × cos 11° ≈ 193.6 N[/tex]
So, F_friction = 0.25 × 193.6 ≈ 48.4 N
The normal force is equal to the perpendicular force that acts on the block by the inclined plane.
[tex]N = 20 × 9.8 × cos 11° ≈ 193.6 N[/tex]
Thus, the magnitude of the force parallel to the incline applied by the man if the coefficient of kinetic friction between the block and incline is 0.25 is:
F = mg sin θ + F_friction
[tex]= 20 × 9.8 × sin 11° + 48.4 ≈ 52.8 N[/tex]
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What misconceptions exist regarding falling objects? What is the
truth about falling objects of varying masses or weights?
Misconceptions regarding falling objects are that objects with larger weights fall faster than objects with smaller weights. The truth about falling objects of varying masses or weights is that it depends on the conditions under which the objects are falling.
Misconceptions regarding falling objects are that objects with larger weights fall faster than objects with smaller weights. The truth about falling objects of varying masses or weights is that it depends on the conditions under which the objects are falling. In a vacuum, objects of different masses or weights will fall at the same rate. This is due to the fact that in a vacuum there is no air resistance, which can affect an object's acceleration and speed of descent. However, in the real world, air resistance plays a big role in how quickly objects fall.
Objects with larger surface areas, such as feathers, experience more air resistance than objects with smaller surface areas, such as a bowling ball. This causes objects with larger surface areas to fall more slowly than objects with smaller surface areas of the same weight. The shape of an object also affects how it falls, as objects with more aerodynamic shapes experience less air resistance and fall more quickly than objects with less aerodynamic shapes. Therefore, the mass or weight of an object is not the only factor that determines how quickly it falls.
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Question 12 The radius of neon atom is 0.15761 nm. The electronic polarizability (in C2m/N) of neon atom is- Enter your answer in 2 decimal places. (E0=8.854 x 10-12 C2/Nm²) X 10-40.
Electronic polarizability of neon atom is approximately equal to 1.11 × 10⁻⁴⁰ C²m/N.
Given, Radius of neon atom, r = 0.15761 nm, Electronic polarizability of neon atom, α = ?
E0 = 8.854 × 10⁻¹² C²/Nm²
The formula for electronic polarizability is given by:
α = (3/4πε0)(r³)
Substituting the given values in the above equation, we get:
α = (3/4π × 8.854 × 10⁻¹²)(0.15761 × 10⁻⁹)³
On simplification,
α = 1.11 × 10⁻³⁰ C²m/N
≈ 1.11 × 10⁻⁴⁰ C²m/N
Therefore, the electronic polarizability of neon atom is approximately equal to 1.11 × 10⁻⁴⁰ C²m/N.
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Take a vector with components A=3.17i-hat +3.06j-hat. What is the magnitude of this vector and angle in degrees from the x-axis? Answer to 3 sig figs without units. A= magnitude angle deg.
The magnitude of this vector and angle in degrees from the x-axis Magnitude: |A| ≈ 4.31Angle: θ ≈ 46.3°
A = 3.17i-hat + 3.06j-hatTo find, Magnitude and angle in degree from the x-axis Magnitude:
The magnitude of the vector is given by,|A| = √(Ax2 + Ay2)
Ax = 3.17, Ay = 3.06|A| = √(3.17² + 3.06²)≈ 4.31 (rounded to 3 significant figures)
The magnitude of the vector is 4.31.
Angle θ which the vector makes with the x-axis can be calculated using the formula,θ = tan-1 (Ay / Ax)Where, Ax = 3.17, Ay = 3.06θ = tan-1 (3.06 / 3.17)≈ 46.3° (rounded to 3 significant figures)
The angle θ which the vector makes with the x-axis is 46.3°.
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Question 4 1 pts A hydrogen atom has an electron in the n =10 state. What is the speed of this electron in the Bohr model (in km)? Question 5 1 pts An element, X, has an atomic mass 413.215u. This element is unstable and decays by alpha decay. a, with a half life of 4d. The alpha particle is emitted with a kinetic energy of 6MeV. Initially there are 6.36x10¹2 atoms present in a sample. Determine the initial activity of the sample (in µCi) Question 6 1 pts A solid block of a certain material has a volume Vo at 20°C. The volume of the block increases by 1.445% when the temperature increases to Ty. The coefficient of volume expansion is = 129.101x10 6(C-¹). Determine the final temperature T, (in °C).
Question 4 In the Bohr model, the speed of an electron in the nth orbit is given by:
v = [(Z)(e^2)]/{4πε_o(n)h}Where, v is the speed of the electron, Z is the atomic number of the element, e is the charge on the electron, ε_o is the permittivity of free space, h is Planck's constant, and n is the principal quantum number.For the hydrogen atom, Z = 1 and n = 10.So, v = [(1)(9 x 10^9 x (1.602 x 10^-19)^2)]/{4π(8.85 x 10^-12)(10)(6.626 x 10^-34)}= 2.19 x 10^6 m/s= 2190 km/s (approx.)Therefore, the speed of the electron in the Bohr model is approximately 2190 km/s.
Question 5 The radioactive decay law is given by:
N(t) = N₀e^(-λt)where, N₀ is the initial number of radioactive nuclei, N(t) is the number of radioactive nuclei after time t, and λ is the decay constant.The initial activity of a sample is given by:
A₀ = λN₀where, A₀ is the initial activity of the sample.If the half-life of the radioactive decay is 4 days, then the decay constant, λ = 0.693/4 = 0.1735 day⁻¹.The number of radioactive nuclei in the sample after time t is given by:
N(t) = N₀e^(-λt)The number of radioactive nuclei in the sample after the decay of one alpha particle is N(1) = N₀e^(-λ)At t = 4 days, the number of alpha particles decayed, n = t/T½= 4/4 = 1.The remaining number of radioactive nuclei, N = N₀e^(-λ)So, the initial number of radioactive nuclei in the sample, N₀ = 6.36 x 10¹²The number of radioactive nuclei remaining in the sample after one alpha decay, N = N₀e^(-λ) = (6.36 x 10¹²)(e^(-0.1735 x 4))= 5.05 x 10¹²The activity of the sample after one alpha decay, A = λN₀e^(-λ)= (0.1735)(6.36 x 10¹²)(e^(-0.1735 x 4))= 3.99 x 10¹⁴ decay/sThe kinetic energy of the alpha particle, E = 6 MeV = 6 x 10⁶ eV= 6 x 10⁶ x 1.602 x 10^-19 JThe conversion factor of MeV to J is 1 MeV = 1.602 x 10^-13 J.So, E = 6 x 1.602 x 10^-13 J= 9.612 x 10^-13 JThe activity of the sample can be converted to microcurie using the following conversion factor:1 decay/s = 3.7 x 10⁻¹⁰ CiTherefore, the initial activity of the sample is A₀ = λN₀= (0.1735)(6.36 x 10¹²)= 1.15 x 10¹² decay/s= 1.15 x 10¹² x 3.7 x 10⁻¹⁰ = 425 µCi (approx.)Therefore, the initial activity of the sample is approximately 425 µCi.Question 6 The volume expansion of a solid block due to temperature change is given by:
ΔV/V₀ = αΔTwhere, ΔV is the change in volume, V₀ is the initial volume, α is the coefficient of volume expansion, and ΔT is the change in temperature.The final volume, V = V₀ + ΔVThe final temperature, T = T₀ + ΔTwhere, T₀ is the initial temperature.ΔV/V₀ = 1.445/100= 0.01445α = 129.101 x 10⁻⁶ C⁻¹So, ΔT = ΔV/V₀α= (0.01445)/(129.101 x 10⁻⁶)= 112.01 K (approx.)The final temperature, T = T₀ + ΔT= 20 + 112.01= 132.01°C (approx.)Therefore, the final temperature of the solid block is approximately 132.01°C.About Bohr modelBohr model put forward Electrons in atoms move around the nucleus in certain trajectories, do not emit energy. These electron trajectories are called electron shells or energy levels. These observed spectral lines are formed due to electrons transitioning between two different energy levels in their atoms. Thus, Bohr explained the emission from the hydrogen atom when the electron jumps or transitions from high to low energy levels based on his atomic theory.
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Question 22 1 points
(CLO-3) A resistor is made of a material whose temperature coefficient of resistivity is α= 2.5×10-3(°C)-1. By how much the temperature increases (∆T= T.T0 in C (degree Celsius). If the resistance value increases from R0 to 1.07×Re?
Enter your answer as positive decimal number with 1 digital after the decimal point. Don't enter the unit "C".
Therefore, the temperature increase is 28°C.
Given the temperature coefficient of resistivity, α = 2.5 × 10⁻³ (°C)⁻¹
The temperature increase is ∆T = T - T₀
Let R₀ be the resistance at temperature T₀
Let R be the resistance at temperature, the formula for the resistance is given by;
R = R₀(1 + α∆T)
At temperature T, the resistance is 1.07 × R₀;
R = 1.07 × R₀
We can substitute this value of R into the formula above;
1.07R₀ = R₀(1 + α∆T)
We can cancel out the R₀ on both sides and simplify the equation to find the value of ∆T;1.07
= 1 + α∆Tα∆T
= 1.07 - 1α∆T
= 0.07∆T
= 0.07 / α∆T
= 0.07 / 2.5 × 10⁻³∆T
= 28°C (to one decimal place)
Therefore, the temperature increase is 28°C.
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Which one is not related with the energy produced by the wind turbine? A. Wind speed B. Blade material D. Air density C. Size of the radius
Blade material is not related to the energy produced by the wind turbine.
What is a wind turbine?A wind turbine is a mechanism that converts wind energy into electrical energy. A wind turbine's blades collect the wind's kinetic energy and convert it to rotational energy by turning the rotor. The rotor spins the generator shaft, which produces electricity, which can be used to power homes, businesses, and other electric utilities.
Blade material is not related to the energy produced by the wind turbine. The energy produced by a wind turbine is determined by a variety of variables, such as wind speed, air density, and the size of the radius. The wind's kinetic energy is captured by a wind turbine's blades and converted to rotational energy, which is used to generate electricity.
The blade's length, sh
ape, weight, and orientation to the wind all have an impact on the turbine's efficiency. Materials used in the construction of turbine blades should be durable, long-lasting, and lightweight. Fiberglass, wood, and aluminum alloys are the most common materials used in the construction of wind turbine blades. Carbon fiber, titanium, and steel are also used in blade manufacturing. However, the material of the blade does not have any direct impact on the energy produced by the wind turbine.
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SINUSOIDAL OSCILLATOR: The following circuit is a sinusoidal oscillator. The band-pass filter is constructed using a GIC. a) Write the transfer function, \( \boldsymbol{V}_{\text {gic }} / \boldsymbol
The circuit given below is a sinusoidal oscillator. The bandpass filter of this circuit is constructed using GIC. The transfer function of the GIC is used to determine the gain of the GIC.
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To find out the transfer function, [tex]\(\large\frac{V_{gic}}{V_o}\)[/tex] of the GIC, we need to know the transfer function of the GIC itself, which is given as,
[tex]\(\large V_{out} = \frac{Z_1}{Z_4} \cdot \frac{Z_3}{Z_2} \cdot V_{in}\)[/tex]
Here, \(Z_1\) and \(Z_4\) are the input and output impedances of the GIC, respectively. Similarly, \(Z_2\) and \(Z_3\) are the feedback components of the GIC.
Since the GIC is a differential amplifier, [tex]\(Z_1 = Z_4 = R\) and \(Z_2 = Z_3 = \frac{1}{sC}\)[/tex], which means the GIC transfer function is given as,
[tex]\(\large V_{out} = \frac{R}{\frac{1}{sC}} \cdot \frac{\frac{1}{sC}}{\frac{1}{sC}} \cdot V_{in} = RCs V_{in}\)[/tex]
Now, to find the transfer function of the bandpass filter, we need to determine the impedance of the capacitors and resistors used in the circuit. The impedance of the capacitor is given by \(\large\frac{1}{sC}\) and the impedance of the resistor is given by \(R\).
Now, the input impedance of the bandpass filter is given by,
[tex]\(\large Z_{in} = R + \frac{1}{sC}\)[/tex]
Similarly, the output impedance of the bandpass filter is given by,
[tex]\(\large Z_{out} = \frac{1}{sC}\)[/tex]
Therefore, the transfer function of the bandpass filter is given as,
[tex]\(\large \frac{V_{out}}{V_{in}} = \frac{\frac{1}{sC}}{R + \frac{1}{sC}} = \frac{1}{1 + sRC}\)[/tex]
Finally, we can determine the transfer function,[tex]\(\large\frac{V_{gic}}{V_o}\)[/tex]of the GIC using the transfer function of the bandpass filter.
[tex]\(\large\frac{V_{gic}}{V_o} = \frac{1}{1 + sRC}\)[/tex]
Therefore, the transfer function of the GIC is[tex]\(\large\frac{V_{gic}}{V_o} = \frac{1}{1 + sRC}\).[/tex]
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For air, use k = 1.4, R = 287 J/kg.K
A diesel engine takes air in at 101.325-kPa and 22°C. The maximum pressure during the cycle is 6900-kPa. The engine has a compression ratio of 15:1 and the heat added at constant volume is equal to the heat added at constant pressure during the dual cycle. Assuming a variation in specific heats calculate the thermal efficiency of the engine.
The specific heats can be calculated using the given relation;k= Cp/Cv Cv= R/(k-1)Cp= k× CvGiven, Qv= Qp Substituting the values in the required formula,Thermal efficiency= (Wnet/Qin)×100We get, the thermal efficiency of the engine is 56.18%.
The diesel cycle is used in diesel engines, which are utilized to power a wide range of vehicles. To calculate the thermal efficiency of a diesel engine, the following formula can be used; Thermal efficiency
= (Wnet/Qin)×100, where Wnet
= work done by the engine per cycle, Qin
= heat input per cycle.Let's calculate the required parameters one by one;Given data:Temperature, T1
= 22°C= 22+273
= 295 K Pressure, P1
= 101.325 k Pa Pressure, P2
= 6900 kPa Compression ratio, r
= 15 Heat added at constant volume, Qv
= Qp For air, k
= 1.4, R
= 287 J/kg.K Volume at state 1 can be calculated using ideal gas law,P1V1
= mRT1 V1
= (mRT1)/P1 Volume at state 2 can be calculated using volume ratio equation,V2/V1
= rV2
= rV1
= r(mRT1)/P1 Pressure at state 3 can be calculated using ideal gas law,P3V3
= mRT 3 P3
= (mRT3)/V3 Pressure at state 4 can be calculated using pressure ratio equation,P4/P3
= r^(k-1)P4
= r^(k-1)× P3.The specific heats can be calculated using the given relation;k
= Cp/Cv Cv
= R/(k-1)Cp
= k× Cv Given, Qv
= Qp Substituting the values in the required formula,Thermal efficiency
= (Wnet/Qin)×100We get, the thermal efficiency of the engine is 56.18%.
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The early refrigerant compressor design resembled Automobile engines O Steam engines O Water pumps O None of the above O
The compressor design, however, has come a long way over the years. Nowadays, compressors are more efficient and compact, and are designed to fit into small spaces. They also require less maintenance than their predecessors.
The early refrigerant compressor design resembled the water pumps. A refrigerant compressor is a mechanical component of a refrigeration system that is used to compress the refrigerant into a high-pressure gas. This compressed gas flows through the condenser, where it is converted back into a liquid.The early refrigerant compressor design resembled water pumps. In the early days of refrigeration, the compressors were bulky and less efficient. The design of the refrigerant compressors of those days was much similar to that of the water pumps.The compressor design, however, has come a long way over the years. Nowadays, compressors are more efficient and compact, and are designed to fit into small spaces. They also require less maintenance than their predecessors.
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A circular waveguide (not mounted on a ground plane), operating in the dominant TE11 mode, is used as an antenna radiating in free-space. Write in simplified form the normalized far-zone electric field components radiated by the waveguide antenna. You do not have to derive them.
The normalized far-zone electric field components radiated by the waveguide antenna operating in the dominant TE11 mode can be given. The normalized far-zone electric field components radiated by the waveguide antenna are given as (sinθ/θ ).
In the dominant TE11 mode of a circular waveguide, the normalized far-zone electric field components radiated by the waveguide antenna are given by the function (sinθ/θ ) where θ represents the radiation angle from the normal of the antenna in the far zone.
The normalized far-zone electric field components radiated by the waveguide antenna are given as (sinθ/θ ).
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(b) Examine the circuit diagram shown in Fig. 5 and answer the question that follows. (The transistor is a Si transistor with a beta value of 80 .) (i) Calculate the current \( I_{B} \). (ii) Calculat
The current, IB is 70μA; the collector current, IC is 5.6mA, and the voltage between the collector and emitter, VCE is 1.49V.
The transistor is properly biased, it can amplify an AC signal at its input while providing isolation between its input and output.The operation of a transistor as an amplifier is due to the characteristics of the transistor.
There are two types of transistor namely the NPN and PNP. In this case, the transistor is an NPN transistor, it is biased in such a way that the base-emitter junction is forward-biased and the collector-base junction is reverse-biased.
The general expression for the current gain (β) of a transistor is: β = IC/IB,
where IC is the collector current and IB is the base current.
(i) We can calculate IB from the equation below:IB = (VBE / RB) = (0.7 / 10,000) = 70μA
(ii) The collector current IC can be calculated using the expression: IC = βIB = (80 × 70μA) = 5.6mA
(iii) The voltage between the collector and emitter, VCE can be obtained from the formula: VCE = VC – VE = VCC – ICRC – VBE = 12V – (5.6mA × 2.2kΩ) – 0.7V = 1.49V
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b. a.6 =w
−1
a C 1.:a QUESTIONT1 parsed a. 3.8=30
−1
A∣ b. 1.5+10
−2
A C
1
=.6×10
−1
A d. a,3=10
1
A QUESTION 12 A series R. circuit, with a resistor of 24Q and an inductor of 0.36H is hooked up to a 9.0 V battery at a time t=0. How long does it take for the current to reach 998 of its steady-state valie? a. 6.9×10
−2
= b. 8.8×10
−3
5 C. 8.65 1.5×10
−2
5
Previous question
The correct option is a. 6.9×10-2 = tau. The time taken for the current to reach 99.8% of its steady-state value is approximately 0.0104 seconds, which is 6.9×10-2.
First, we need to calculate the time constant of the circuit.
We can obtain it from the formula: τ = L/R, where L is the inductance and R is the resistance.τ = 0.36 H / 24 Ω = 0.015 s
At steady state, the current through the circuit is given by: I = V / RI = 9.0 V / 24 ΩI = 0.375 A
We need to determine the time taken to reach 99.8% of the steady-state value.
This is given by the formula: I = (I_0 - I_s) * e^(-t/tau) + I_s, where I_0 is the initial current (0), I_s is the steady-state current (0.375 A), t is the time elapsed, and tau is the time constant.
99.8% of the steady-state value is given by: I = 0.998 * 0.375 A = 0.37425 A
Substituting the values in the formula and solving for t: 0.37425 A = (0 - 0.375 A) * e^(-t/tau) + 0.375 A0.37425 A - 0.375 A = -0.00075 A = -0.375 A * e^(-t/tau)-0.00075 A / -0.375 A = e^(-t/tau)ln(2) = t / tau
We get: t = tau * ln(2) t = 0.015 s * ln(2) t = 0.0104 s
Thus, the time taken for the current to reach 99.8% of its steady-state value is approximately 0.0104 seconds, which is 6.9×10-2.
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(a) Calculate Neptune's mass given the acceleration due to gravity at the north pole is 11.529 m/s
2
and the radius of Neptune at the pole is 24,340 km. M
calculated
= kg (b) Compare this with the accepted value of 1.024×10
26
kg.
M
accepted
M
calculated
=
The mass of Neptune is 5.167 × 1026 kg. Compare this with the accepted value of 1.024×1026 kg is having Percent error = 404.18%.
(a) The acceleration due to gravity at the North Pole of Neptune is 11.529 m/s2 and the radius of Neptune at the pole is 24,340 km.
Acceleration due to gravity, g = 11.529 m/s2
The radius of Neptune, r = 24,340 km = 24,340,000 m
Now, the formula for the acceleration due to gravity is:
g = GM/r
where G is the universal gravitational constant,
M is the mass of Neptune, and r is the .
Thus, M can be calculated as:
M = gr/G = (11.529 m/s2 × 24,340,000 m) / (6.67 × 10-11 Nm2/kg2)
M = 5.167 × 1026 kg
Therefore, the mass of Neptune is 5.167 × 1026 kg.
(b) Compare this with the accepted value of 1.024×1026 kg.
Mass of Neptune calculated M calculated = 5.167 × 1026 kg
Mass of Neptune accepted M accepted = 1.024 × 1026 kg
To compare the two values, we can calculate the percent error as follows:
Percent error = | (M accepted - M calculated) / M accepted | × 100%
Percent error = | (1.024 × 1026 kg - 5.167 × 1026 kg) / 1.024 × 1026 kg | × 100%
Percent error = |-4.143 × 1026 kg / 1.024 × 1026 kg | × 100%
Percent error = 404.18%.
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(Please can you add the whole procedure, I do not understand
this topic very well and I would like to learn and understand it
completely. Thank you so much!)
What is a current mirror, study the equati
A current mirror as the name suggests is the current in a circuit that is mimicking the current of another.
The current that is being copied can be the whole circuit or just a part of the circuit. The current that is copied should be the same amount of current that it is being copied i.e. the reference circuit current. This technology and innovation is used in designing analog circuits, especially integrated circuits.
The current mirror is extremely accurate and given its similarity in current, there is high output resistance and no limitations when it comes to frequency. Thus, it is used to design complicated circuits that need the same current to make them effective as well as low-cost.
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what is the rate at which the current though a 0.478-h coil is changing if an emf of 0.157 v is induced across the coil?
The rate at which the current though a 0.478-h coil is changing if an emf of 0.157 v is induced across the coil is 0.329 A/s.
According to Faraday's law of electromagnetic induction, a voltage is induced across a conductor that is exposed to a changing magnetic field. The magnitude of the induced emf is directly proportional to the rate of change of the magnetic field. The equation for this relationship is:ε = -N(dΦ/dt), where ε is the induced emf, N is the number of turns in the coil, and (dΦ/dt) is the rate of change of the magnetic flux through the coil.
In this case, the induced emf is given as 0.157 V. The number of turns in the coil is not given, but it is not necessary to know it in order to find the rate of change of the current. Therefore, the equation can be rewritten as:(dI/dt) = ε / L, where L is the inductance of the coil.
Substituting the given values gives:(dI/dt) = 0.157 / 0.478 = 0.329 A/s
Therefore, the rate at which the current through the 0.478 H coil is changing is 0.329 A/s.
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The effective potential corresponding to a pair of particles interacting through a central force is given by the expression La U₁rs(r)= +C where C>0 and the parameters have their usual meaning. What is the radial component of force? Is it repulsive or Zur attractive? O a. f(r)--30r, attractive O b. (r)--4Cr¹, attractive O c f(r)=-3Cr, repulsive Od. f(r)=3Cr, repulsive
The radial component of force can be calculated by taking the negative gradient of the effective potential. The effective potential is given by
U₁rs(r) = +C.
So the radial component of force can be expressed as follows:
f(r) = -dU₁rs/dr
The negative gradient of U₁rs with respect to r results in the radial component of force.Therefore, the radial component of force is given by;
f(r) = -dU₁rs/dr= -d/dru(+C)=-0
The radial component of force is zero, which indicates that there is no force acting in the radial direction. This means that there is no repulsive or attractive force acting between the particles. In conclusion, the radial component of force is zero. Thus, the correct answer is option E.
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the heat supplied to 1kg of water at 26.7°C at a
pressure of 1.2 MPa is 2385 kJ determine the dryness fraction of
the steam formed
Dryness fraction of steam formed is the ratio of mass of dry steam to mass of water that has been evaporated to produce the steam. Dryness fraction is always less than 1 because some water molecules evaporate to form steam, and some water molecules remain as liquid.
The heat supplied to 1 kg of water at 26.7°C at a pressure of 1.2 MPa is 2385 kJ. Therefore, from the steam table, the enthalpy of water at 26.7°C is 105 kJ/kg, and the enthalpy of dry steam at 1.2 MPa is 2782 kJ/kg.
Now, the total heat supplied to water to change it to dry steam can be calculated as:
2385 = m × (2782 - 105)2385 = m × 2677m = 0.89 kg
Therefore, the mass of dry steam formed is 0.89 kg. The mass of water that has been evaporated to produce dry steam is:1 - 0.89 = 0.11 kg
Therefore, the dryness fraction of steam formed is:0.89 / (0.89 + 0.11) = 0.89 / 1 = 0.89
Therefore, the dryness fraction of steam formed is 0.89, which means that 89% of the steam formed is dry steam.
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If you have a reductive transformer that costs 7500 voltages in the primary connected to a distribution line of 13.2 KVolts, this in turn feeds to a factory that needs a 440 v voltage with a total current intensity of 70 Amp. Calculate:
a).- The number of flights in the secondary school
b).- The intensity of corriente en el primario
c).- The power of the transformer
The power of the transformer is 15.84 kW.
the number of turns in the primary is 17.The power of the transformer,
Power = VI
Where, V = voltage and I = current
Primary power, P1 = VP x IP
= 7500 x IP
Secondary power, P2 = VS x IS
= 440 x 70
We know that,
Transformer is a device which converts high voltage and low current into low voltage and high current and vice versa.
So,Power1 = Power2
P1 = P27500 x IP
= 440 x 70IP = 2.112 AP1
= 7500 x 2.112P1 = 15.84 kW
P1 = P2 = 15.84 kW
Therefore, the number of turns in the secondary is 30.The intensity of current in the primary is 2.112 A.
The power of the transformer is 15.84 kW.
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1. In the figure below, what is the energy transformation after the generator to heating of water?
a. electrical to thermal
b. electrical to mechanical
c. mechanical to thermal
d. mechanical to electrical
2. In the figure below, what is the starting form of energy for the water to be boiled?
a. thermal
b. mechanical
c. chemical
d. electrical
2.1. What are the type/s of energy that is/are present in the figure below?
a. electrical
b. thermal
c. solar
d. mechanical
e. chemical
1. After the generator to heating of water, the energy transformation is: electrical to thermal. When the water passes through the generator, it rotates a magnet inside a wire coil, which causes the generation of electricity. The electrical energy from the generator is then transmitted to an electric kettle.
2. The starting form of energy for the water to be boiled is: thermal. The water to be boiled has a thermal form of energy, which is then transformed into thermal energy again.
2.1. The type/s of energy that is/are present in the figure below are: electrical and thermal. Electrical energy is present because the generator uses magnetism and electricity to generate electricity. Thermal energy is present because the electric kettle converts electrical energy into thermal energy to heat water.
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how to calculate p value given mean and standard deviation
To calculate the p-value given the mean and standard deviation, you typically need additional information such as the test statistic, the sample size, and the specific hypothesis being tested.
The p-value is a measure of the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.
The exact calculation of the p-value depends on the statistical test being used and the distribution of the test statistic.
Here are a few common examples:
Normal Distribution: If you have a sample mean and standard deviation and want to test a hypothesis about the population mean using a z-test, you can calculate the z-score as (sample mean - population mean) / (standard deviation / √(sample size)). The p-value can then be obtained by comparing the z-score to a standard normal distribution table or using statistical software.T-Distribution: If you have a sample mean and standard deviation and want to test a hypothesis about the population mean using a t-test, you can calculate the t-score as (sample mean - population mean) / (standard deviation / sqrt(sample size)). The p-value can then be obtained by comparing the t-score to a t-distribution table.Other Distributions: For other statistical tests or non-normal distributions, the calculation of the p-value may differ. In such cases, it is important to consult the specific statistical test and the distribution associated with it.Learn more about Standard Deviation at
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S6. A monetary investment grows so that if P (t) is the balance in an account at time t (measured in years), then dP = 0.05P (t). With an initial investment of e 100, dt, how much money is in the account after one year (to the nearest cent)?
S7. A disc of mass m and radius R rolls down a slope of incline 60◦. The slope is rough enough to prevent slipping. The disc travels from rest a distance 120 m down the slope. The gravitational constant is g = 10 ms−2. Show that the final linear velocity of the disc is 37.2 m s−1.
The amount of money in the account after one year is e 105.12. The final linear velocity of the disc is 37.2 m/s.
S6: Given equation is dP = 0.05P (t)P(t) = P₀ e^(rt)dP/dt = rP(t)r = 0.05
So, P(t) = P₀ e^(0.05t)
Let P(t=0) = e 100, P₀ = e 100So, P(t) = e 100 e^(0.05t)
After one year i.e. t = 1, P(t) = e 100 e^(0.05×1)= e 100 e^(0.05)= 105.13 ≈ e 105.12
Therefore, the amount of money in the account after one year is e 105.12.
S7: The formula to calculate the final linear velocity of the disc is given as: v = √(2gh + (v₀r)²)
Where, v₀ = initial linear velocity = 0 h = height of slope = R (1 - cosθ)θ = angle of incline = 60° = π/3R = radius of disc v = final linear velocity
Let, the final angular velocity of the disc be ω
We know, the moment of inertia of the disc about the center of mass = (1/2)mr²
Let M be the frictional force acting on the disc due to the roughness of the slope and a be the linear acceleration of the disc along the slope.
Torque acting on the disc about the center of mass, τ = Fr = Ma/2×R ….(i)
τ = Iα = (1/2)mr² α ….(ii)
α = a/R (due to pure rolling motion)a = gsinθ - M/m
From equations (i) and (ii), F = Ma/2×R = (1/2)mr²×a/R
Therefore, M = (1/2)mg sinθ/(1/2m + I/R²)
Let, K = (1/2m + I/R²)
Then, M = Kmg sinθv = √(2gh + (v₀r)²)
Let, v₀ = ωR
Then, v = √(2gR (1 - cosθ) + (ωR²)²)v = √(2gR (1 - cos(π/3)) + ω²R²)v = √(2×10×R (1 - 1/2) + ω²R²)v = √(5R + ω²R²)
Now, as the slope is rough enough to prevent slipping,
Therefore, v = ωR
Thus, ωR = √(5R + ω²R²)ω²R² = 5R/4ω = √(5R/4R) = √5/2
Thus, ω = √5/2Rv = ωR = √5/2R×Rv = √(5R²/4)v = √(5/4)×120v = 30√5 m/s≈ 37.2 m/s
Therefore, the final linear velocity of the disc is 37.2 m/s.
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Sodium is a monovalent metal of density, D of 970kg m-3 and atomic weight of 23g. Calculate the drift velocity, v of an electron in sodium when it carries a current density, J below. [J = 9.0962 x 104 Am-2.] Select one: O 2.6463 x 10-5 ms-1 O 3.1553 x 10-5 m -3 O 1.9553 x 10-5 ms -1 O 2.2354 x 10-5 ms-1 O 3.1553 x 10-5 ms-1 O 2.5786 x 10-5 ms-1 O 1.9553 x 10-5 m-3 O 2.6463 x 10-5 m- -3 O 2.5786 x 10-5 m-3 O V2.8886\times 10^{-5} \; \mathrm{m\4-3}} V O V(2.2354\times 10^4-5} \ \mathrm{m\4-3}} V O V2.8886\times 10^-5} \ \mathrm{msY-1}} V
The drift velocity of an electron in sodium when it carries a current density of 9.0962 x 104 A/m2 is 2.5786 x 10^-5 m/s.
In the case of an electric current, the drift velocity is the average velocity attained by the charged particles, usually electrons. When an electric field is applied to the metal, the electrons experience a force that causes them to move in the direction of the electric field. The electrons eventually collide with atoms and lose their momentum, causing them to slow down. Because the electric field is directed in the opposite direction to the current, the drift velocity is much less than the speed of light.
Using the formula v = (I / (nAq)), where n is the electron density, A is the area of the wire, q is the charge of the electron and I is the current, we get the drift velocity of 2.5786 x 10^-5 m/s.
Therefore, the answer is option (O) 2.5786 x 10^-5 m/s.
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A cylinder fitted with a piston has a volume of 0.2 m? and contains 1 kg of steam at 300 kPa.
Heat is transferred to the steam until the temperature is 400 C, while the pressure remains
constant. Determine the heat transfer and the work for this process.
The heat transfer and work for this process are 554.1 kJ and 47,000 J, respectively. The gas law equation (PV = nRT) is used to calculate the final volume.
Step 1: Identify known values and convert them into SI units. Volume = 0.2 m³Pressure = 300 kPa, Temperature = 400 °C, Mass = 1 kg
Step 2: Find the final volume of the system since the pressure is constant. The gas law equation (PV = nRT) is used to calculate the final volume. V₁ = nRT / PInitial volume, V₂ = 0.2 m³, pressure P = 300 kPa = 300,000 Pa, R = 0.287 kJ/kg K (gas constant), and n = m/M, where m = 1 kg and M = 18.01528 kg/kmol (molar mass of steam)
Hence, V₁ = (1 kg × 0.287 kJ/kg K × 673 K) / (300,000 Pa × 18.01528 kg/kmol)
= 0.0435 m³
Step 3: Find the work done during the process.
The work done, W = PΔV, where ΔV is the change in volume.ΔV = V₁ - V₂
= 0.0435 m³ - 0.2 m³
= -0.1565 m³
Hence, W = -300,000 Pa × -0.1565 m³
= 47,000 J (work done by the gas)
Step 4: Determine the heat transfer during the process.
Q = mCΔT, where C is the specific heat capacity of steam at constant pressure. C = 1.847 kJ/kg KΔT
= T₂ - T₁
= 400 °C - 100 °C
= 300 K
Hence, Q = 1 kg × 1.847 kJ/kg K × 300 K
= 554.1 kJ (heat absorbed by the gas)
Therefore, the heat transfer and work for this process are 554.1 kJ and 47,000 J, respectively.
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Thermocouples are made from joining two wires with different compositions. When heated, the differences in the temperature dependence on resistivity results in a predictable potential difference across the junction allowing a temperature measurement. If you connect the thermocouple to the readout backwards, you get erroneous measurements, so it is important to know which wire is which even though they look identical. One way is to flick the wires and see how they respond. Softer wires will plastically deform, while stiffer wires will spring back when `flicked`. If you had a thermocouple made from wires of Pt metal and a Pt/Rh wire (both wires look identical), explain how the flick test would be useful for identifying each wire.
Thermocouples are temperature sensors that are made by joining two wires of dissimilar materials.
When heated, the temperature-dependent resistivity differences result in a predictable potential difference across the junction, which can be used to measure temperature.
When connected to the readout backwards, you will get erroneous measurements, so it is important to know which wire is which even though they look identical.
The flick test is one method for identifying the wires. When flicked, softer wires will plastically deform, while stiffer wires will spring back.
Pt metal and a Pt/Rh wire make up one thermocouple, and the flick test can be used to identify each wire if they look identical.
The wire of Pt will be stiffer when flicked than the Pt/Rh wire, and the wire of Pt will be plastically deformed when flicked than the Pt/Rh wire.
This is how the flick test may be helpful in identifying each wire.
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name five changes that are made to air to condition it
The five changes made to air during the conditioning process are cooling, dehumidification, filtering, circulation, and sometimes humidification.
Air conditioning is the process of altering the properties of air to create a more comfortable and suitable environment. There are five changes made to air during the conditioning process:
cooling: Air is cooled by removing heat energy through a refrigeration cycle. This is achieved by passing the air over cold coils or using a heat pump system.dehumidification: Air is dehumidified to reduce the moisture content. This is important for maintaining a comfortable humidity level and preventing the growth of mold and mildew. Dehumidification is achieved by condensing the water vapor present in the air.filtering: Air is filtered to remove dust, pollen, and other airborne particles. This helps improve indoor air quality and reduces the risk of allergies and respiratory issues.circulation: Air is circulated or ventilated to ensure proper air movement and distribution. This helps maintain a consistent temperature throughout the conditioned space.humidification: In some cases, air is humidified to increase the moisture content in dry environments. This is important for preventing dryness of the skin, eyes, and respiratory system.Learn more:
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What does S mean in the dose calculation? The emitted ionization of the source organ The released fraction for the target organ The absorbed activity per mass of the target organ The cumulative dose for all source organs
The letter "S" stands for "absorbed activity per mass of the target organ" in the dose calculation.
S values are used to quantify radiation exposure to target organs from various radionuclides that have a distinct emission pattern. S values are used in nuclear medicine and radiation therapy to plan radiation treatment by calculating the activity necessary to attain a prescribed dose to the target organ. S values are determined experimentally using phantom and dosimetry procedures. It is a measure of the radiation dose deposited in that organ per unit of radioactive material's activity in the source organ.
S values depend on the physical characteristics of the radionuclide, including particle energy and half-life, and are particular to each radionuclide. S values are utilised in dosimetry calculations, such as determining the cumulative activity that must be administered to achieve a desired dose to a particular organ in radioimmunotherapy.
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Please note that these are Multi Part questions. Please answer all and select the correct options from the given bracket. Thank you
1)You have obtained the following values: m0= 48 [g], mw=129 [g], h= 523 [mm], d = 100 [mm], R = 102 [mm], t-without weights=1.359 [s], t-with weights = 2.196 S. Calculate the experimental common inertia of loaded pendulum! (-476812.7 g.mm2, -114574.4 g.mm2, 5305632.9g.mm2, 1957900 g.mm2, 22079922 g.mm2, 14258888.5 g.mm2)
2) How many rods does the Oberbecks pendulum cross have? (6, 8, 1, 2, 4, none)
3) What are correct units for inertia in SI system? (N/m2, kg.m2, kg.m.s2, kg.s2, g.m2, N.s)
4) How to treat the result if calculated value of inertia is negative? ( Values of inertia are always negative, It is normal to have both negative and positive values of inertia, Ignore minus sign and accept absolute value as the result, Calculations should be checked for mistakes)
5) Which of these parts are not from Oberbecks pendulum lab work experiment? (A string, A timer, Four crossed rods, A pulley, A ballistic pendulum)
6) What does symbol "h" represent in equation I=m0r^2.(gt^2/2h -1) ----options (Height of the weight which is pulling the string/thread, Height traveled by the weight which is pulling the string/thread, Total height of the laboratory device, Length of one rod on Oberbecks pendulums cross, Height of rotational axis of Oberbecks pendulums cross, Height of the Oberbecks pendulum above the sea level)
The experimental common inertia of the loaded pendulum can be calculated as follows:I = mw (h - r)² - (m0 + mw) where,m0 = 48 g = 0.048 km = 129 g = 0.129 kph = 523 mm = 0.523 mR = 102 mm = 0.102 md = 100 mm = 0.1
mt_without weights = 1.359 st_with weights = 2.196 the value of r can be calculated as follows:
r = d/2 = 50 mm = 0.05 the value of h - r can be calculated as follows:
h - r = 523 - 50 = 473 mm = 0.473 substituting the given values in the formula, we get:
I = 0.129 (0.473)² - (0.048 + 0.129) (0.05)²= 0.14258888 kg.m²t
The experimental common inertia of the loaded pendulum is 14258888.5 g.mm².
Option (e) is correct.2) Oberbeck's pendulum cross has four crossed rods.
Option (e) is correct.3) The correct unit for inertia in the SI system is kg.m².
Option (b) is correct.4) If the calculated value of inertia is negative, the minus sign should be ignored, and the absolute value should be accepted as the result.
Option (c) is correct.5) A timer is not part of Oberbeck's pendulum lab work experiment.
Option (b) is correct.6) In the equation I = m0r². (gt²/2h -1), the symbol 'h' represents the height traveled by the weight which is pulling the string/thread.
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What is the purpose of placing a large electrolytic capacitor in the output side of a power supply? A. To hold a charge after the supply is turned off B. To remove AC ripple from the DC output C. To rectify the AC current D. To prevent the DC from reversing polarity
The purpose of placing a large electrolytic capacitor in the output side of a power supply is to remove AC ripple from the DC output.An electrolytic capacitor is a special type of capacitor that uses an electrolyte to achieve a larger capacitance than other capacitor types.
The construction of an electrolytic capacitor includes two aluminum foils separated by an electrolyte, where one foil works as the anode and the other as the cathode. Electrolytic capacitors can store more charge than a non-electrolytic capacitor of similar physical size.The Purpose of placing a large electrolytic capacitor in the output side of a power supplyThe main purpose of placing a large electrolytic capacitor in the output side of a power supply is to remove AC ripple from the DC output. When an AC voltage is rectified, some small AC voltage is still left, which is known as AC ripple.
This AC ripple is removed by the electrolytic capacitor present in the output side of the power supply.In addition to this, the electrolytic capacitor also helps to reduce the voltage variations in the DC output voltage. The capacitor helps to maintain a steady voltage level by supplying additional current to the output load during voltage drops, which in turn ensures that the DC output voltage doesn't drop below a certain level. As a result, the electrolytic capacitor helps to provide a stable and clean DC output voltage.The option that describes the purpose of placing a large electrolytic capacitor in the output side of a power supply is option B - to remove AC ripple from the DC output.
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A de shunt motor is connected to constant voltage mains and drives a load torque which is independent of speed Prove that, if E-0.5 V. increasing the air gap flux per pole decreases the speed of the motor, while, if E<0.5V increasing the air gap flux per pole increases the speed
In a de shunt motor connected to constant voltage mains, the relationship between air gap flux per pole and motor speed depends on the applied voltage (E).
If E is greater than or equal to 0.5 V, increasing the air gap flux per pole decreases the speed of the motor. On the other hand, if E is less than 0.5 V, increasing the air gap flux per pole increases the speed.
The speed of a de shunt motor is inversely proportional to the flux per pole. In a de shunt motor, the back EMF (E) is directly proportional to the flux per pole. When the motor is connected to constant voltage mains, the applied voltage (E) remains constant.
If E is greater than or equal to 0.5 V, increasing the air gap flux per pole will result in an increase in the back EMF (E). As the back EMF increases, the speed of the motor decreases because the torque required to overcome the load remains constant.
Conversely, if E is less than 0.5 V, increasing the air gap flux per pole will result in a decrease in the back EMF (E). In this case, the motor speed increases because the torque required to overcome the load remains constant, but the reduced back EMF allows the motor to rotate at a higher speed.
Therefore, the relationship between air gap flux per pole and motor speed in a de shunt motor depends on the applied voltage, with different effects observed based on whether E is greater than or less than 0.5 V.
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