Q. No.
In an adiabatic expansion of a gas, if the initial and final temperatures are \(T_1\) and \(T_2\), respectively, then the change in internal energy of the gas is:
1. \(\frac{nR}{\gamma-1}(T_2-T_1)\)
2. \(\frac{nR}{\gamma-1}(T_1-T_2)\)
3. \(nR ~(T_1-T_2)\)
4. Zero
1. \(\frac{nR}{\gamma-1}(T_2-T_1)\)
2. \(\frac{nR}{\gamma-1}(T_1-T_2)\)
3. \(nR ~(T_1-T_2)\)
4. Zero
One mole of an ideal gas at an initial temperature of T K does 6R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of the gas will be:
1. (T + 2.4)K
2. (T – 2.4)K
3. (T + 4)K
4. (T – 4)K
In a cyclic process, the internal energy of the gas:
| 1. | Increases | 2. | Decreases |
| 3. | Remains constant | 4. | Becomes zero |
In a Carnot engine, when \(T_2=0^\circ \mathrm{C}\) and \(T_1=200^\circ \mathrm{C},\) its efficiency is \(\eta_1\) and when \(T_1=0^\circ \mathrm{C}\) and \(T_2=-200^\circ \mathrm{C},\) its efficiency is \(\eta_2.\) What is the value of \(\frac{\eta_1}{\eta_2}?\)
| 1. | 0.577 | 2. | 0.733 |
| 3. | 0.638 | 4. | cannot be calculated |
When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is?
| 1. | \(2 \over 5\) | 2. | \(3 \over 5\) |
| 3. | \(3 \over 7\) | 4. | \(5 \over 7\) |
A closed hollow insulated cylinder is filled with gas at \(0^{\circ}\mathrm{C}\) and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \(100^{\circ}\mathrm{C}\).
If the piston moves 5 cm, the length of the hollow cylinder will be:
1. 13.65 cm
2. 27.3 cm
3. 38.6 cm
4. 64.6 cm
A monoatomic gas is supplied with the heat \(Q\) very slowly, keeping the pressure constant. The work done by the gas will be:
1. \({2 \over 3}Q\)
2. \({3 \over 5}Q\)
3. \({2 \over 5}Q\)
4. \({1 \over 5}Q\)
The molar heat capacity in case of a diatomic gas if it does a work of when heat Q is supplied to it is:
1.
2.
3.
4.
A cyclic process for 1 mole of an ideal gas is shown in the V-T diagram. The work done in AB, BC and CA respectively is:
| 1. | \(0, R T_2 \ln \left(\frac{V_1}{V_2}\right), R\left(T_1-T_2\right)\) |
| 2. | \(R\left(T_1-T_2\right), 0, R T_1 \ln \frac{V_1}{V_2}\) |
| 3. | \(0, R T_2 \ln \left(\frac{V_2}{V_1}\right), R\left(T_1-T_2\right)\) |
| 4. | \(0, R T_2 \ln \left(\frac{V_2}{V_1}\right), R\left(T_2-T_1\right)\) |
The Carnot cycle (reversible) of gas is represented by a pressure-volume curve as shown. Consider the following statements:
| I. | Area ABCD = Work done on the gas |
| II. | Area ABCD = Net heat absorbed |
| III. | Change in the internal energy in cycle = 0 |
Which of the statement(s) given above is/are correct?
| 1. | I only | 2. | II only |
| 3. | II and III | 4. | I, II and III |
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