The PV diagram of an ideal gas is shown in the figure. The work done by the gas in the process $1\to 2\to 3\to 4$ is given by:

          

1.	\(\frac{9}{2}P_0V_0\)	2.	\(\frac{15}{2}P_0V_0\)
3.	\(\frac{13}{2}P_0V_0\)	4.	\(\frac{3}{2}P_0V_0\)

A pressure \((P)\) versus volume \((V)\) graph is obtained for an ideal gas from state \(A\) to state \(B\) (as shown in the figure below). Which of the following is the correct statement?
             

When the sink temperature is kept at \(400~\text{K},\) the efficiency of a Carnot engine is \(50\text{%}.\) While keeping the source temperature constant, by how much should we reduce the sink temperature to increase the efficiency to \(60\text{%}\text{?}\)

Which of the following graph shows the variation of pressure P with volume V for an ideal gas at a constant temperature?

1.		2.
3.		4.

A gas performs the minimum work when it expands:

An ideal gas goes from \(A\) to \(B\) via two processes, \(\mathrm{I}\) and \(\mathrm{II},\) as shown. If \(\Delta U_1\) and \(\Delta U_2\) are the changes in internal energies in processes \(\mathrm{I}\) and \(\mathrm{II},\) respectively,  (\(P:\) pressure, \(V:\) volume) then:

An ideal monoatomic gas \(\left(\gamma = \frac{5}{3}\right )\) absorbs 50 cal in an isochoric process. The increase in internal energy of the gas is:

The pressure-temperature \((P\text-T)\) graph for two processes, \(A\) and \(B,\) in a system is shown in the figure. If \(W_1\) and \(W_2\)${\mathrm{}}_{}$ are work done by the gas in process \(A\) and \(B\) respectively, then:

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.

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: