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. \(3456~\text{J}\)

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:  
         

In the \((P\text-V)\) diagram shown, the gas does \(5~\text J\) of work in the isothermal process \(ab\) and \(4~\text J\) in the adiabatic process \(bc.\) What will be the change in internal energy of the gas in the straight path from \(c\) to \(a?\) 

             
1. \(9~\text J\)
2. \(1~\text J\)
3. \(4~\text J\)
4. \(5~\text J\)

\(ABCA\) is a cyclic process. Its \(P\text-V\) graph would be:

1.		2.
3.		4.

A thermodynamic system undergoes a cyclic process \(ABCDA\) as shown in Fig. The work done by the system in the cycle is: 
             
1. \( P_0 V_0 \)
2. \( 2 P_0 V_0 \)
3. \( \frac{P_0 V_0}{2} \)
4. zero

The efficiency of an ideal heat engine (Carnot heat engine) working between the freezing point and boiling point of water is:
1. \(26.8\%\)
2. \(20\%\)
3. \(6.25\%\)
4. \(12.5\%\)