The figure shows the \((P\text-V)\) diagram of an ideal gas undergoing a change of state from \(A\) to \(B\). Four different paths \(\mathrm{I, II, III}\) and \(\mathrm{IV}\), as shown in the figure, may lead to the same change of state.
               

Which of the following options contains only correct statements?

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. $P_0{V}_0$

A given mass of gas expands from state A to state B by three paths, 1, 2 and 3, as shown in the figure. If ${\mathrm{W}}_1,$ ${\mathrm{W}}_2$ $\mathrm{and}$ ${\mathrm{W}}_3$ respectively be the work done by the gas along the three paths, then:

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:

The pressure of a monoatomic gas increases linearly from $4\times {10}^5$ N/m² to $8\times {10}^5$ N/m² when its volume increases from 0.2 m³ to 0.5 m³. The work done by the gas is:

1. $2.8\times {10}^5 \mathrm{J}$

2. $1.8\times {10}^6 \mathrm{J}$

3. $1.8\times {10}^5 \mathrm{J}$

4. $1.8\times {10}^2 \mathrm{J}$

Two identical samples of a gas are allowed to expand, (i) isothermally and (ii) adiabatically. Work done will be:

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: