Q. No.| 1. | \(300R \) | 2. | \(300R ~\mathrm{ln}(2) \) |
| 3. | \(300 ~\mathrm{ln}(6) \) | 4. | \(300R~\mathrm{ln}(7) \) |
An ideal gas undergoes a cyclic process as depicted on the pressure \((P)\) versus volume \((V)\) graph.
During which part of the process is no work done on or by the gas?
1. \(AB\)
2. \(BC\)
3. \(CD\)
4. \(DE\)
(Given : \(\mathrm{R}=8.31 \mathrm{Jk}^{-1} \mathrm{~mol}^{-1}\))
A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in the figure. Its volume is then reduced to the original value from \(E\) to \(F\) by an isobaric process. The total work done by the gas from \(D\) to \(E\) to \(F\) is:
1. \(600 ~\text{J}\)
2. \(300 ~\text{J}\)
3. \(450 ~\text{J}\)
4. \(500 ~\text{J}\)
A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180~\text{J}\). The gas absorbs \(250~\text{J}\) of heat along the path \(ab\) and \(60~\text{J}\) along the path \(bc\). The work done by the gas along the path \(abc\) is:
1. \(140~\text{J}\)
2. \(130~\text{J}\)
3. \(100~\text{J}\)
4. \(120~\text{J}\)
1. \(14PV\)
2. \(7PV\)
3. \(3PV\)
4. \(8PV\)
| (A) | \(\Large\frac{nR(T_1-T_2)}{\gamma-1}\) | (B) | \(\Large\frac{P_1V_1-P_2V_2}{\gamma-1}\) |
| (C) | \(\Large\frac{P_1V_1+P_2V_2}{\gamma+1}\) | (D) | \(n\gamma R(T_1-T_2)\) |
| 1. | (A), (B) and (C) |
| 2. | (A) and (B) only |
| 3. | (C) and (D) only |
| 4. | (B), (C) and (D) only |
A gas undergoes a thermodynamic process from state \((P_1,V_1,T_1)\) to state \((P_2,V_2,T_2).\) The process satisfies the relation: \(PV^{3/2}=\text{constant}.\)
The work done by the gas in this process is:
| 1. | \(\dfrac{\left(P_2 V_2-P_1 V_1\right)}{2}\) | 2. | \(\dfrac{\left(P_1 V_1-P_2 V_2\right)}{2}\) |
| 3. | \(\dfrac{3\left(P_1 V_1-P_2 V_2\right)}{2}\) | 4. | \({2}\left(P_1 V_1-P_2 V_2\right)\) |
1.\(\begin{equation} { RT }[2-\sqrt{2}] \end{equation}\)
2. \(\begin{equation} {RT}[2+\sqrt{2}] \end{equation}\)
3. \(\begin{equation} \dfrac{{T}}{{R}}[2+\sqrt{2}] \end{equation}\)
4. \(\begin{equation} \dfrac{R}{T}[2-\sqrt{2}] \end{equation}\)
1. \(6 P_0 V_0\)
2. \(-2 P_0 V_0 \)
3. \(+2 P_0 V_0 \)
4. \(+4 P_0 V_0\)
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