An ideal gas goes from A to B via two processes, l and ll, as shown. If $∆{\mathrm{U}}_1$ and $∆{\mathrm{U}}_2$ are the changes in internal energies in processes I and II, respectively, then (\(P:\) pressure, \(V:\) volume)

The incorrect relation is:
(where symbols have their usual meanings)

1. ${\mathrm{C}}_{\mathrm{P}}=\frac{\mathrm{\gamma R}}{\mathrm{\gamma }-1}$

2. ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\mathrm{R}$

3. $∆\mathrm{U}=\frac{{\mathrm{P}}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}}-{\mathrm{P}}_{\mathrm{i}}{\mathrm{V}}_{\mathrm{i}}}{1-\mathrm{\gamma }}$

4. ${\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{\gamma }-1}$

If n moles of an ideal gas is heated at a constant pressure from 50°C to 100°C, the increase in the internal energy of the gas will be: \(\left(\frac{C_{p}}{C_{v}} = \gamma\   and\   R = gas\   constant\right)\)

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is?

Two cylinders contain the same amount of an ideal monoatomic gas. The same amount of heat is given to two cylinders. If the temperature rise in cylinder A is T₀, then the temperature rise in cylinder B will be:

1. $\frac{4}{3}{\mathrm{T}}_0$

2. $2{\mathrm{T}}_0$

3. $\frac{{\mathrm{T}}_0}{2}$

4. $\frac{5}{3}{\mathrm{T}}_0$

The specific heat of a gas in an isothermal process is: 
1. Infinite
2. Zero
3. Negative
4. Remains constant

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 \(\mathrm{A}\) to state \(\mathrm{B}\) will be: