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Q. No.The ratio of molar specific heat capacity at constant pressure (\(C_p\)) to that at constant volume (\(C_v\)) varies with temperature (\(T\)) as: (assume temperature is low)
1. \(T^0\)
2. \(T^{\frac{1}{2}}\)
3. \(T^1\)
4. \(T^{\frac{3}{2}}\)
Subtopic: Molar Specific Heat |
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A diatomic gas is taken from point \(A\) to point \(B\) in a thermodynamic process as described in the pressure−volume graph shown. The change in internal energy is equal to:
1. \(3.75 \times 10^6 ~\text{J}\)
2. \(2.25 \times 10^6 ~\text{J}\)
3. \(7.5 \times 10^6 ~\text{J}\)
4. \(4.5 \times 10^6 ~\text{J}\)
1. \(3.75 \times 10^6 ~\text{J}\)
2. \(2.25 \times 10^6 ~\text{J}\)
3. \(7.5 \times 10^6 ~\text{J}\)
4. \(4.5 \times 10^6 ~\text{J}\)
Subtopic: Types of Processes |
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During an adiabatic process performed on a diatomic gas \(725\) J of work is done on the gas. The change in internal the energy of the gas is equal to:
1. \(495\) J
2. \(725\) J
3. \(225\) J
4. \(0\)
1. \(495\) J
2. \(725\) J
3. \(225\) J
4. \(0\)
Subtopic: First Law of Thermodynamics |
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A Carnot engine working between a source and a sink at \(200~\text K\) has an efficiency of \(50\%.\) Another Carnot engine working between the same source and another sink with an unknown temperature \(T\) has an efficiency of \(75\text{%}.\) The value of \(T\) is equal to:
1. \(400 ~\text K\)
2. \(300 ~\text K\)
3. \(200 ~\text K\)
4. \(100 ~\text K\)
1. \(400 ~\text K\)
2. \(300 ~\text K\)
3. \(200 ~\text K\)
4. \(100 ~\text K\)
Subtopic: Carnot Engine |
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In the series sequence of two engines \(E_1\) and \(E_2\) as shown. \(T_1=600\) K and \(T_2=300\) K. It is given that both the engines working on the Carnot principle have the same efficiency, then temperature \(T\) at which exhaust of \(E_1\) is fed into \(E_2\) is equal to:
1. \(300 \sqrt{2}\) K
2. \(200 \sqrt{2}\) K
3. \(300 \sqrt{3}\) K
4. \(200 \sqrt{3}\) K
1. \(300 \sqrt{2}\) K
2. \(200 \sqrt{2}\) K
3. \(300 \sqrt{3}\) K
4. \(200 \sqrt{3}\) K
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In a polytropic process, the pressure \(P\) varies with volume \(V\) according to the equation \(P=aV^{-3},\) where \(a\) is a constant. The bulk modulus of this system is:
1. \(3V\)
2. \(3P\)
3. \(P\)
4. \(V\)
1. \(3V\)
2. \(3P\)
3. \(P\)
4. \(V\)
Subtopic: Types of Processes |
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A mixture of gases with adiabatic coefficient equal to 3/2 is compressed from initial state (P0, V0) to one fourth volume adiabatically. Its final pressure will be equal to
1. P0
2. 2P0
3. 4P0
4. 8P0
1. P0
2. 2P0
3. 4P0
4. 8P0
Subtopic: Types of Processes |
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Given below are two statements:
| Assertion (A): | When heat is supplied to a system, its temperature must increase. |
| Reason (R): | Positive work done by the system increases the volume of the thermodynamic system. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Work Done by a Gas |
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A Carnot engine operates between temperatures of \(27^\circ \mathrm C\) and \(127^\circ \mathrm C\) and performs \(2\) kJ of work. The amount of heat energy rejected is:
| 1. | \(4\) kJ | 2. | \(6\) kJ |
| 3. | \(8\) kJ | 4. | \(12\) kJ |
Subtopic: Carnot Engine |
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Given a cyclic process shown in an indicator diagram using SI units. The work done by the gas during the process is:
| 1. | \(300\) units | 2. | \(-300\) units |
| 3. | \(600\) units | 4. | \(-600\) units |
Subtopic: Cyclic Process |
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