# An ideal heat engine (Carnot engine) working between temperatures $$T_1$$ and $$T_2$$ has an efficiency $$\eta.$$ The new efficiency if both the source and sink temperatures are doubled will be: 1. $$\frac{\eta}{2}$$ 2. $$\eta$$ 3. $$2\eta$$ 4. $$3\eta$$

Subtopic:  Carnot Engine |
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A monoatomic ideal gas, initially at temperature $$T_1$$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $$T_2$$ by releasing the piston suddenly. If $$L_1$$ and $$L_2$$ are the lengths of the gas column before and after expansion, respectively, then $$\frac{T_1}{T_2}$$ is given by:
1. $$\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}$$
2. $$\frac{L_1}{L_2}$$
3. $$\frac{L_2}{L_1}$$
4. $$\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}$$

Subtopic:  Types of Processes |
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An insulator container contains 4 moles of an ideal diatomic gas at a temperature T. If heat Q is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms, but the temperature of the gas remains constant, then:
1. Q = 2RT
2. Q = RT
3. Q = 3RT
4. Q = 4RT

Subtopic:  First Law of Thermodynamics |
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The volume of air (diatomic) increases by $$5\%$$ in its adiabatical expansion. The percentage decrease in its pressure will be:

 1 $$5\%$$ 2 $$6\%$$ 3 $$7\%$$ 4 $$8\%$$
Subtopic:  Types of Processes |
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Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at $$T_1=800$$ K and rejects to sink at $$T_2$$ K. The second engine, B, receives heat rejected by the first engine and rejects to another sink at $$T_3=300$$ K. If the work outputs of the two engines are equal, then the value of $$T_2$$ will be:

 1 100 K 2 300 K 3 550 K 4 700 K
Subtopic:  Carnot Engine |
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The initial pressure and volume of a gas are $$P$$ and $$V$$, respectively. First, it is expanded isothermally to volume $$4V$$ and then compressed adiabatically to volume $$V$$. The final pressure of the gas will be: [Given: $$\gamma = 1.5$$]

 1 $$P$$ 2 $$2P$$ 3 $$4P$$ 4 $$8P$$
Subtopic:  Types of Processes |
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A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $$62^{\circ}\mathrm{C}$$, the efficiency of the engine is doubled. The temperatures of the source and sink are:
1. $$80^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}$$
2. $$95^{\circ}\mathrm{C}, 28^{\circ}\mathrm{C}$$
3. $$90^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}$$
4. $$99^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}$$

Subtopic:  Carnot Engine |
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An ideal gas is taken from point A to point B, as shown in the P-V diagram. The work done in the process is:

1. $\left({P}_{A}-{P}_{B}\right)\left({V}_{B}-{V}_{A}\right)$
2. $\frac{1}{2}\left({P}_{B}-{P}_{A}\right)\left({V}_{B}+{V}_{A}\right)$
3. $\frac{1}{2}\left({P}_{B}-{P}_{A}\right)\left({V}_{B}-{V}_{A}\right)$
4. $\frac{1}{2}\left({P}_{B}+{P}_{A}\right)\left({V}_{B}-{V}_{A}\right)$

Subtopic:  Work Done by a Gas |
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If the temperature of the source and the sink in the heat engine is at 1000 K & 500 K respectively, then the efficiency can be:
1. 20%
2. 30%
3. 50%
4. All of these

Subtopic:  Carnot Engine |
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In an adiabatic process, the graph for work done versus change of temperature $$\Delta T$$ will be:
 1 2 3 4
Subtopic:  Work Done by a Gas |
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