Q. No.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.
\(8P\)
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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. \(99^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)
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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.
2.
3.
4.
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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
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In an adiabatic process, the graph for work done versus change of temperature ∆T will be:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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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. | \(\frac{25 nγR}{\gamma - 1}\) |
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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. | \(\frac{7}{2}P(V_1-V_2)\) |
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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 \(\eta_\mathrm x\) and\(\eta_\mathrm y\). 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 |
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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 |
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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. | \(8\%\) |
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