The volume \((V)\) of a monatomic gas varies with its temperature \((T),\) as shown in the graph. The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state \(A\) to state \(B\) will be:
             

1.	\(\dfrac{2}{5}\)	2.	\(\dfrac{2}{3}\)
3.	\(\dfrac{1}{3}\)	4.	\(\dfrac{2}{7}\)

A thermodynamic system undergoes a cyclic process \(ABCDA\) as shown in Fig. The work done by the system in the cycle is: 

One mole of an ideal gas expands at a constant temperature of \(300~\text{K}\) from an initial volume of \(10\) litres to a final volume of \(20\) litres. The work done in expanding the gas is equal to:
(\(R = 8.31\) J/mole-K)
1. \(750~\text{J}\)
2. \(1728~\text{J}\)
3. \(1500~\text{J}\)
4. \(3456~\text{J}\)

A sample of \(0.1\) g of water at \(100^{\circ}\mathrm{C}\)$$ and normal pressure (\(1.013 \times10^5\) N m^–2) requires \(54\) cal of heat energy to convert it into steam at \(100^{\circ}\mathrm{C}\)$$. If the volume of the steam produced is \(167.1\) cc, then the change in internal energy of the sample will be:

The pressure of a monoatomic gas increases linearly from $\mathrm{}$\(4\times 10^5~\text{N/m}^2\) to $\mathrm{}$\(8\times 10^5~\text{N/m}^2\) when its volume increases from \(0.2 ~\text m^3\) to \(0.5 ~\text m^3.\) The work done by the gas is:
1. \(2 . 8 \times10^{5}~\text J\)
2. \(1 . 8 \times10^{6}~\text J\)
3. \(1 . 8 \times10^{5}~\text J\)
4. \(1 . 8 \times10^{2}~\text J\)$\mathrm{}$

A horizontal cylinder has two sections of unequal cross-sections in which two pistons, A and B, can move freely. The pistons are joined by a string. Some gas is trapped between the pistons. If this gas is heated, the pistons will: