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Q. No.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. \(100 ~\text K\)
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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A monoatomic gas initially at pressure \(P\) and volume \(V\) is compressed to \(\left ( \frac{1}{8} \right )^\mathrm{th}\)of its volume adiabatically. The final pressure of the gas is:
| 1. | \(4P\) | 2. | \(8P\) |
| 3. | \(16P\) | 4. | \(32P\) |
Subtopic: Work Done by a Gas |
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When the amount of heat supplied to a gas in a system is equal to \(1000\) J, the system in return does \(200\) J of work on the surrounding. What would be the change in the internal energy of the gas?
1. \(800\) J
2. \(1200\) J
3. \(1000\) J
4. \(1100\) J
1. \(800\) J
2. \(1200\) J
3. \(1000\) J
4. \(1100\) J
Subtopic: First Law of Thermodynamics |
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In which of the following processes does the internal energy of a gas remain constant?
1. Isothermal
2. Isochoric
3. Isobaric
4. Adiabatic
1. Isothermal
2. Isochoric
3. Isobaric
4. Adiabatic
Subtopic: Types of Processes |
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