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:
1. $104.3$ J
2. $208.7$ J
3. $42.2$ J
4. $84.5$ J

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:
             

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. $12.5\%$

Thermodynamic processes are indicated in the following diagram: 
   
Match the following:  

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:

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

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then,