Question

When the temperature of 4 moles of a gas was increased from \(70^{\circ }\)C to \(90^{\circ }\)C, at constant volume, the change in internal energy was \(60\text{ J}\). The total heat capacity of the gas at constant volume is

• A. \(0.5\text{ J/K}\)
• B. \(2\text{ J/K}\)
• C. \(3\text{ J/K}\)
• D. \(4\text{ J/K}\)

Hint:

At constant volume the heat supplied equals the change in internal energy. Divide by the temperature change.

Answer 1

The Correct Option is C

Step 1: Formula first
Total heat capacity $=nC_v$, so $\Delta U=nC_v\Delta T$.

Step 2: Substitute
$60=(nC_v)\times20$

Step 3: Result
$nC_v=3\text{ J/K}$. The number of moles is already included in the total heat capacity.

Final Answer:
The heat capacity comes out to 3 J/K. \[ \boxed{\text{(C) }3\text{ J/K}} \]