Question

$70\text{cal}$ of heat is required to raise the temperature of $2$ moles of an ideal gas at constant pressure from ${30}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$. The amount of heat required to raise the temperature of the same gas through same range of temperature (${30}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$) at constant volume is
Given $(\gamma =7/5)$

• A. $30\text{cal}$
• B. $50\text{cal}$
• C. $70\text{cal}$
• D. $90\text{cal}$

Answer 1

The correct option is B $50\text{cal}$

Heat absorbed at constant pressure to increase the temperature by $\Delta T$,
$Q_p=n{C}_p\Delta T...\left(i\right)$
$C_p=$molar heat capacity at constant pressure
$\Rightarrow$Heat required to raise the temperature of same gas by $\Delta T$ at constant volume is,
$Q_V=n{C}_V\Delta T...\left(ii\right)$
$C_V=$molar heat capacity at constant volume
$\Rightarrow \frac{Q_V}{Q_p}=\frac{C_V}{C_p}$
$Q_V=Q_p\times \frac{C_V}{C_p}$
$Q_V=70\times \frac{1}{\gamma }$
$\therefore Q_V=70\times \frac{5}{7}=50\text{cal}$