- 1(current)
Q. No.| Assertion (A): | Internal energy of an ideal gas does not change when it is taken through a cyclic process. |
| Reason (R): | Internal energy is a state function, and when the gas returns to the same state – it attains the same value independent of the process. |
Choose the correct option from the given ones:
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
In the diagrams (i) to (iv) , variation of volume with changing pressure is shown. A gas is taken along the path ABCDA. The change in internal energy of the gas will be
(1) Positive in all cases (i) to (iv)
(2) Positive in cases (i), (ii) and (iii) but zero in (iv) case
(3) Negative in cases (i), (ii) and (iii) but zero in (iv) case
(4) Zero in all four cases
The ratio of the temperatures at \(B,A\) i.e., \(T_B/T_A\) equals:
1. \(2\)
2. \(\dfrac12\)
3. \(4\)
4. \(\dfrac14\)
In each of the four diagrams \((\mathrm a)\) to \((\mathrm d),\) the variation of pressure \(p\) with volume \(V\) is shown as a closed path. The gas undergoes a cyclic process along the path \(ABCDA.\) What will be the net change in the internal energy of the gas after completing one full cycle in each case?
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| \((\mathrm a)\) | \((\mathrm b)\) |
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| \((\mathrm c)\) | \((\mathrm d)\) |
| 1. | The change in internal energy is zero in all four cases. |
| 2. | Positive in cases \((\mathrm a),(\mathrm b)\) and \((\mathrm c),\) but zero in case \((\mathrm d).\) |
| 3. | Negative in cases \((\mathrm a),(\mathrm b)\) and \((\mathrm c),\) but zero in the case \((\mathrm d).\) |
| 4. | Positive in all cases from \((\mathrm a)\) to \((\mathrm d).\) |
| (i) | process \(AB\) – Isobaric expansion quadrupling the volume |
| (ii) | process \(BC\) – Isochoric cooling |
| (iii) | process \(CA\) – Adiabatic compression |
| (A) | For this gas, \(C_V=2R\) |
| (B) | \(C_P=3R\) |
| (C) | \(\gamma=\dfrac32\) |
| 1. | (A) and (C) only |
| 2. | (B) and (C) only |
| 3. | (A) and (B) only |
| 4. | (A), (B) and (C) |
The heat supplied to the gas in the process \(AB\) equals:
1. \(\dfrac52p_0V_0\)
2. \(2p_0V_0\)
3. \(\dfrac32p_0V_0\)
4. \(p_0V_0\)
The volume of the gas at \(C\) is:
1. \(4V_0\)
2. \(3V_0\)
3. \(2V_0\)
4. \(\dfrac{3V_0}{2}\)
If \(Q\), \(E\), and \(W\) denote respectively the heat added, the change in internal energy, and the work done in a closed cycle process, then:
| 1. | \(W=0\) | 2. | \(Q=W=0\) |
| 3. | \(E=0\) | 4. | \(Q=0\) |
A thermodynamic system is taken through the cycle PQRSP process. The net work done by the system is -
(1) 20 J
(2) – 20 J
(3) 400 J
(4) – 374 J
| 1. | \(2 {PV}\) | 2. | \(4{PV}\) |
| 3. | \(\frac{1}{2}{PV}\) | 4. | \(PV\) |
- 1(current)
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