In the given (V-T) diagram, what is the relation between pressures ${\mathrm{P}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{P}}_2$?

     

1. ${\mathrm{P}}_2<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{P}}_1$

2. ${\mathrm{P}}_2<mspace\; width="1em"></mspace><<mspace\; width="1em"></mspace>{\mathrm{P}}_1$

3. Cannot be predicted

4. ${\mathrm{P}}_2<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{P}}_1$

When $1<mspace\; width="1em"></mspace>\mathrm{kg}$ of ice at $0°\mathrm{C}$ melts to water at $0°\mathrm{C}$, the resulting change in its entropy, taking latent heat of ice to be $80<mspace\; width="1em"></mspace>\mathrm{cal}/\mathrm{g}$ is

1.  $273<mspace\; width="1em"></mspace>\mathrm{cal}/\mathrm{K}$

2.  $8<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^4<mspace\; width="1em"></mspace>\mathrm{cal}/\mathrm{K}$

3.  $80<mspace\; width="1em"></mspace>\mathrm{cal}/\mathrm{K}$

4.  $293<mspace\; width="1em"></mspace>\mathrm{cal}/\mathrm{K}$

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

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

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. \(R\)

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. \(12.5\%\)

An ideal gas is compressed to half its initial volume using several processes. Which of the processes results in the maximum work done on the gas?
1. adiabatic
2. isobaric
3. isochoric
4. isothermal