At a pressure of \(2\) atmospheres, a mass of diatomic gas \((\gamma = 1.4)\), is compressed adiabatically, causing its temperature to rise from \(27^{\circ}\mathrm{C}\) to \(927^{\circ}\mathrm{C}\). The pressure of the gas in the final state is:
1. 8 atm
2. 28 atm
3. 68.7 atm
4. 256 atm
A monoatomic gas at pressure P1 and volume V1 is compressed adiabatically to 1/8th its original volume. What is the final pressure of the gas?
1. P1
2. 16 P1
3. 32 P1
4. 64 P1
An ideal gas goes from state \(A\) to state \(B\) via three different processes as indicated in the \((P\text-V)\) diagram.
If \(Q_1,Q_2,Q_3\) indicate the heat absorbed by the gas along the three processes and \(\Delta U_1, \Delta U_2, \Delta U_3\) indicate the change in internal energy along the three processes respectively, then:
1. | \(Q_3>Q_2>Q_1\) and \(\Delta U_1= \Delta U_2= \Delta U_3\) |
2. | \(Q_1=Q_2=Q_3\) and \(\Delta U_1> \Delta U_2> \Delta U_3\) |
3. | \(Q_3>Q_2>Q_1\) and \(\Delta U_1> \Delta U_2> \Delta U_3\) |
4. | \(Q_1>Q_2>Q_3\) and \(\Delta U_1= \Delta U_2= \Delta U_3\) |
1. | \(10~\text{J}\) | 2. | \(12~\text{J}\) |
3. | \(36~\text{J}\) | 4. | \(6~\text{J}\) |
The molar specific heat at a constant pressure of an ideal gas is \(\dfrac{7}{2}R.\) The ratio of specific heat at constant pressure to that at constant volume is:
1. | \(\dfrac{7}{5}\) | 2. | \(\dfrac{8}{7}\) |
3. | \(\dfrac{5}{7}\) | 4. | \(\dfrac{9}{7}\) |
A Carnot engine whose sink is at \(300~\mathrm{K}\) has an efficiency of \(40\)%. By how much should the temperature of the source be increased to increase its efficiency by \(50\)% of its original efficiency?
1. | \(275~\mathrm{K}\) | 2. | \(325~\mathrm{K}\) |
3. | \(250~\mathrm{K}\) | 4. | \(380~\mathrm{K}\) |
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. | \(Q=0\) |
In thermodynamic processes which of the following statements is not true?
1. | In an adiabatic process, the system is insulated from the surroundings. |
2. | In an isochoric process, pressure remains constant. |
3. | In an isothermal process, the temperature remains constant. |
4. | In an adiabatic process \(PV^\gamma=\mathrm{constant}.\) |
The internal energy change in a system that has absorbed \(2\) kcal of heat and done \(500\) J of work is:
1. \(8900\) J
2. \(6400\) J
3. \(5400\) J
4. \(7900\) J