Question

40 calories of heat is needed to raise the temperature of $1mol$ of an ideal monoatomic gas from ${20}^{\circ }C$ to ${30}^{\circ }C$ at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $(R=2cal/mo{l}^{-1}{K}^{-1})$ is :

• A. $20cal$
• B. $40cal$
• C. $60cal$
• D. $80cal$

Answer 1

The correct option is A $20cal$

At constant pressure, the amount of heat required is

$Q=n{C}_p\Delta T$

$40=1\times C_p\times 10$

Thus, $C_p=4$

Now, $\gamma =\frac{C_p}{C_v}$

$\gamma$ for monoatomic gas $=1.67$

Thus, $C_v=\frac{C_p}{\gamma }=\frac{4}{1.67}=2.4$

For a constant volume process,

$Q=n{C}_v\Delta T$

Thus,

$Q=1\times 2.4\times 10$

$Q=24cal\approx 20cal$

Hence Option C