Work done during the given cycle is:
                               
1. 4$P_0{V}_0$

2. 2$P_0{V}_0$

3. $\frac{1}{2}$$P_0{V}_0$

4. $P_0{V}_0$

An ideal gas goes from A to B via two processes, l and ll, as shown. If $∆{\mathrm{U}}_1$ and $∆{\mathrm{U}}_2$ are the changes in internal energies in processes I and II, respectively, then (\(P:\) pressure, \(V:\) volume)

The pressure-temperature (P-T) graph for two processes, A and B, in a system is shown in the figure. If ${\mathrm{W}}_1$ and ${\mathrm{W}}_2$ are work done by the gas in process A and B respectively, then:

1. ${\mathrm{W}}_1$ = ${\mathrm{W}}_2$

2. ${\mathrm{W}}_1$ < ${\mathrm{W}}_2$

3. ${\mathrm{W}}_1$ > ${\mathrm{W}}_2$

4. ${\mathrm{W}}_1$ = - ${\mathrm{W}}_2$

Heat is supplied to a diatomic gas in an isochoric process. The ratio $∆\mathrm{Q}:\hspace{0.17em}∆\mathrm{U}$ is: (symbols have usual meanings)

1. 5 : 3

2. 5: 2

3. 1: 1

4. 5: 7

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

If an ideal gas undergoes two processes at constant volumes ${\mathrm{V}}_1$ $\mathrm{and}$ ${\mathrm{V}}_2$ as shown in the pressure-temperature (P-T) diagram, then:

1. ${\mathrm{V}}_1$ = ${\mathrm{V}}_2$

2. ${\mathrm{V}}_1$ > ${\mathrm{V}}_2$

3. ${\mathrm{V}}_1$ < ${\mathrm{V}}_2$

4. ${\mathrm{V}}_1\ge {\mathrm{V}}_2$

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

1. 129.6 J

2. $-$129.6 J

3. 149.6 J

4. $-$149.6 J

The efficiency of an ideal heat engine is less than 100% because of:

The first law of thermodynamics is based on:

Find out the total heat given to diatomic gas in the process A$\to$B$\to$C : (B$\to$C is isothermal)
                 

1. ${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0$ $\ln 2$

2. $\frac{1}{2}$${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0\ln 2$

3. $\frac{5}{2}$${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0$ $\ln 2$

4. 3${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0$ $\ln 2$