The figure below shows two paths that may be taken by gas to go from state \(A\) to state \(C\).
In process \(AB\), \(400~\text{J}\) of heat is added to the system, and in process \(BC\), \(100~\text{J}\) of heat is added to the system. The heat absorbed by the system in the process \(AC\) will be:
1. \(380~\text{J}\)
2. \(500~\text{J}\)
3. \(460~\text{J}\)
4. \(300~\text{J}\)
A monoatomic gas at a pressure \(P\), having a volume \(V\), expands isothermally to a volume \(2V\) and then adiabatically to a volume \(16V\). The final pressure of the gas is: \(\left(\text{Take:}~ \gamma = \frac{5}{3} \right)\)
1. | \(64 ~P\) | 2. | \(32~P\) |
3. | \(\frac{P}{64}\) | 4. | \(16~P\) |
A thermodynamic system undergoes a cyclic process \(ABCDA\) as shown in Fig. The work done by the system in the cycle is:
1. \( P_0 V_0 \)
2. \( 2 P_0 V_0 \)
3. \( \frac{P_0 V_0}{2} \)
4. zero
1. | \(1000~\text{J}\) | 2. | zero |
3. | \(-2000~\text{J}\) | 4. | \(2000~\text{J}\) |
1. | \(\frac{R}{\gamma -1}\) | 2. | \(\frac{\gamma -1}{R}\) |
3. | \(\gamma R \) | 4. | \(\frac{\left ( \gamma -1 \right )R}{\left ( \gamma +1 \right )}\) |
A thermodynamic system is taken through the cycle \(\mathrm{ABCD}\) as shown in the figure. Heat rejected by the gas during the cycle is:
1. \(2 {PV}\)
2. \(4{PV}\)
3. \(\frac{1}{2}{PV}\)
4. \(PV\)
One mole of an ideal gas goes from an initial state \(A\) to the final state \(B\) with two processes. It first undergoes isothermal expansion from volume \(V\) to \(3V\) and then its volume is reduced from \(3V\) to \(V\) at constant pressure. The correct \((P-V)\) diagram representing the two processes is:
1. | 2. | ||
3. | 4. |
When \(1\) kg of ice at \(0^{\circ}\) C melts into the water at \(0^{\circ}\) C, the resulting change in its entropy, taking the latent heat of ice to be \(80\) cal/gm, is:
1. \(8\times 10^4\) cal/K
2. \(80\) cal/K
3. \(293\) cal/K
4. \(273\) cal/K
During an isothermal expansion, a confined ideal gas does -150 J of work against its surrounding. This implies that:
1. | 300 J of heat has been added to the gas. |
2. | no heat is transferred because the process is isothermal. |
3. | 150 J of heat has been added to the gas. |
4. | 150 J of heat has been removed from the gas. |