Question

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

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

Answer 1

Answer: (A)

$20cal$

Number of moles $n=1$

Change in temperature $\Delta T=10K$
At constant pressure, heat absorbed $Q_p=n{C}_p\Delta T$

$\therefore$ $40=1\times C_p\times 10$

$⟹$ $C_p=4$ $cal-mo{l}^{-1}{K}^{-1}$

Since $R=2cal-mo{l}^{-1}{K}^{-1}$

We get $C_p=2R$
Using $C_p-C_v=nR$

$\therefore$ $2R-C_v=1\times R$ $⟹C_v=R=2cal-mo{l}^{-1}{K}^{-1}$
At constant volume, heat absorbed $Q_v=n{C}_v\Delta T$

$⟹$ $Q_v=1\times 2\times 10=20cal$