Question

70 calorie of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from ${40}^o$ C to ${45}^o$ C.

Find the amount of heat required to raise the temperature of the same gas through the same range at constant volume:

[R = 2 cal/mol-K]

Answer 1

Given :

$T_1={40}^{o}C$

$T_2={45}^{o}C$

$n=2$

$\therefore$ $\Delta T=T_2-T_1=45-40=5$

Heat supplied at constant pressure

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

$\therefore$ $70=2\times C_p\times 5$

$⟹C_p=7$ $cal/mol-K$

Using $C_p-C_v=nR$

where $R=2$ $cal/mol-K$

$⟹$ $7-C_v=2\times 2$

Thus $C_v=3$ $cal/mol-K$

Heat supplied at constant volume

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

$⟹$$Q_v=2\times 3\times 5=30$ cal

Hence, the amount of heat required to raise the temperature of the same gas through the same range at constant volume is 30 cal