The molar specific heat at a constant pressure of an ideal gas is \(\frac{7}{2}R.\) The ratio of specific heat at constant pressure to that at constant volume is:
1. \(\frac{7}{5}\)
2. \(\frac{8}{7}\)
3. \(\frac{5}{7}\)
4. \(\frac{9}{7}\)

A Carnot engine whose sink is at \(300~\mathrm{K}\) has an efficiency of \(40\)%. By how much should the temperature of the source be increased to increase its efficiency by \(50\)% of its original efficiency?

In thermodynamic processes which of the following statements is not true?

One mole of an ideal gas goes from an initial state \(A\) to the final state \(B\) with two processes. It first undergoes isothermal expansion from volume \(V\) to \(3V\) and then its volume is reduced from \(3V\) to \(V\) at constant pressure. The correct \((P-V)\) diagram representing the two processes is:

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

One mole of an ideal monatomic gas undergoes a process described by the equation \(PV^3=\mathrm{constant}.\) The heat capacity of the gas during this process is:
1. \(\frac{3}{2}R\)
2. \(\frac{5}{2}R\)
3. \(2R\)
4. \(R\)

\(1\) g of water of volume \(1\) cm³ at \(100^\circ \text{C}\) is converted into steam at the same temperature under normal atmospheric pressure \(\approx 1\times10^{5} \) Pa. The volume of  steam formed equals \(1671\) cm³. If the specific latent heat of vaporization of water is \(2256\) J/g, the change in internal energy is:
1. \(2423\) J
2. \(2089\) J
3. \(167\) J
4. \(2256\) J

If an average person jogs, he produces \(14.5 \times10^3\) cal/min. This is removed by the evaporation of sweat. The amount of sweat evaporated per minute (assuming \(1\) kg requires \(580 \times10^3\) cal for evaporation) is:
1. \(0.25\) kg
2. \(0.50\) kg
3. \(0.025\) kg
4. \(0.20\) kg

The first law of thermodynamics is a statement of: