Question

$140\text{cal}$ of heat is required to raise the temperature of $2$ mole of a diatomic gas at constant pressure from $0^{\circ }\text{C}$ to ${10}^{\circ }\text{C}$. How much heat will be required to rise its temperature from $0^{\circ }\text{C}$ to ${10}^{\circ }\text{C}$ at constant volume?

• A. $60\text{cal}$
• B. $100\text{cal}$
• C. $140\text{cal}$
• D. $180\text{cal}$

Answer 1

The correct option is B $100\text{cal}$

At constant pressure,
$C_P=\frac{Q}{n\Delta \theta }=\frac{140}{2\times 10}{\text{cal/mol-}}^{\circ }\text{C}=7{\text{cal/mol-}}^{\circ }\text{C}$

$C_v=C_p-R=7-2=5{\text{cal/mol-}}^{\circ }\text{C}$

At constant volume,
Required quantity of heat $Q=n{C}_v\Delta \theta =2\times 5\times 10\text{cal}=100\text{cal}$