# 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 ∆T will be:

 1 2 3 4
Subtopic:  Work Done by a Gas |
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If n moles of an ideal gas is heated at a constant pressure from 50°C to 100°C, the increase in the internal energy of the gas will be: $$\left(\frac{C_{p}}{C_{v}} = \gamma\ and\ R = gas\ constant\right)$$

 1 $$\frac{50 nR}{\gamma - 1}$$ 2 $$\frac{100 nR}{\gamma - 1}$$ 3 $$\frac{50 nγR}{\gamma - 1}$$ 4 $$\frac{25 nγR}{\gamma - 1}$$
Subtopic:  Molar Specific Heat |
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In the P-V graph shown for an ideal diatomic gas, the change in the internal energy is:

 1 $$\frac{3}{2}P(V_2-V_1)$$ 2 $$\frac{5}{2}P(V_2-V_1)$$ 3 $$\frac{3}{2}P(V_1-V_2)$$ 4 $$\frac{7}{2}P(V_1-V_2)$$
Subtopic:  Molar Specific Heat |
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Two Carnot engines x and y are working between the same source temperature $$T_1$$ and the same sink temperature $$T_2$$${}_{}$. If the temperature of the source in Carnot engine x is increased by $$\Delta T$$, and in the Carnot engine y, the temperature of the sink is increased by$$\Delta T$$, then the efficiency of x and y becomes $$\eta_\mathrm x$$${\mathrm{}}_{}$ and$$\eta_\mathrm y$$${\mathrm{}}_{}$. Then:

 1 $$\eta_{\mathrm{x}}=\eta_{\mathrm{y}}$$ 2 $$\eta_{\mathrm{x}}<\eta_{\mathrm{y}}$$ 3 $$\eta_{\mathrm{x}}>\eta_{\mathrm{y}}$$ 4 The relation between $$\eta_{\mathrm{x}}$$ and $$\eta_{\mathrm{y}}$$ depends on the nature of the working substance

Subtopic:  Carnot Engine |
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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 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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