If an ideal gas undergoes two processes at constant volumes \(V_1~\text{and}~V_2\) as shown in the pressure-temperature \((P\text-T)\) diagram, then:

             
1. \(V_1= V_2\)
2. \(V_1> V_2\)
3. \(V_1< V_2\)
4. \(V_1\ge V_2\)

The internal energy of an ideal gas increases in:

1. Adiabatic expansion

2. Adiabatic compression

3. Isothermal expansion

4. Isothermal compression

\(0.04\) mole of an ideal monatomic gas is allowed to expand adiabatically so that its temperature changes from \(800~\text{K}\) to \(500~\text{K}.\) The work done during expansion is nearly equal to:

Which of the following is true for the molar heat capacity of an ideal gas?

A heat engine is working between 200 K and 400 K. The efficiency of the heat engine may be:

1. 20%

2. 40%

3. 50%

4. All of these

In the cyclic process shown in the pressure-volume \((P-V)\) diagram, the change in internal energy is equal to:

1. $\pi {\left(\frac{{\mathrm{P}}_2-{\mathrm{P}}_1}{2}\right)}^2$

2. $\mathrm{\pi }{\left(\frac{{\mathrm{V}}_2-{\mathrm{V}}_1}{2}\right)}^2$

3. $\frac{\mathrm{\pi }}{4}({\mathrm{P}}_2-{\mathrm{P}}_1)({\mathrm{V}}_2-{\mathrm{V}}_1)$

4. zero

When a system is moved from state \(a\) to state \(b\) along the path \(acb\), it is discovered that the system absorbs \(200~\text{J}\) of heat and performs \(80~\text{J}\) of work.  Along the path \(adb\), heat absorbed \(Q =144~\text{J}\). The work done along the path \(adb\) is:

The variation of molar heat capacity at constant volume ${\mathrm{C}}_{\mathrm{V}}$ with temperature T for a monatomic gas is:

1.		2.
3.		4.