Let $∆{\mathrm{U}}_1$ and $∆{\mathrm{U}}_2$ be the changes in internal energy of an ideal gas system in the processes A and B as shown in the figure, then (P: pressure, V: Volume)

1. $∆{\mathrm{U}}_1$ > $∆{\mathrm{U}}_2$

2. $∆{\mathrm{U}}_1$ =$∆{\mathrm{U}}_2$

3. $∆{\mathrm{U}}_1$ <$∆{\mathrm{U}}_2$

3. $∆{\mathrm{U}}_1\ne ∆{\mathrm{U}}_{2_{}}$

When heat \(Q\) is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by \(\Delta T\). the heat required to produce the same change in temperature, at a constant pressure is:
1. \( \frac{7}{5} Q \)
2. \(\frac{3}{2} Q \)
3. \( \frac{2}{3} Q \)
4. \( \frac{5}{3} Q\)
 

A diatomic gas, having \(C_P=\dfrac{7}{2}R\) and \(C_V=\dfrac{5}{2}R\) is heated at constant pressure. The ratio of \(dU:dQ:dW\) is:
1. \(5:7:3\)
2. \(5:7:2\)
3. \(3:7:2\)
4. \(3:5:2\)

n moles of an ideal gas is heated at constant pressure
from 50°C to 100°C, the increase in internal energy
of the gas is $\left(\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}=\mathrm{\gamma }<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{R}=\mathrm{gas}<mspace\; width="1em"></mspace>\mathrm{constant}\right)$

1. $\frac{50<mspace\; width="1em"></mspace>\mathrm{nR}}{\mathrm{\gamma }-1}$

2. $\frac{100<mspace\; width="1em"></mspace>\mathrm{nR}}{\mathrm{\gamma }-1}$

3. $\frac{50<mspace\; width="1em"></mspace>\mathrm{n\gamma R}}{\mathrm{\gamma }-1}$

4. $\frac{25<mspace\; width="1em"></mspace>\mathrm{n\gamma R}}{\mathrm{\gamma }-1}$