Question

Six moles of oxygen gas is heated from \(20^{\circ }\)C to \(35^{\circ }\)C at constant volume. If specific heat capacity at constant pressure is \(8\text{ cal mol}^{-1}\text{k}^{-1}\) and gas constant is \(2\text{ cal mol}^{-1}\text{k}^{-1}\). The change in internal energy of the gas is

• A. \(180\) cal
• B. \(300\) cal
• C. \(360\) cal
• D. \(540\) cal

Hint:

Find Cv from Cp minus R, then use change in internal energy equal to n Cv times the temperature change.

Answer 1

The Correct Option is D

Step 1: Formula-first
At constant volume $Q=\Delta U=nC_v\Delta T$.

Step 2: Substitution
$n=6$, $C_v=C_p-R=6$, $\Delta T=15$.

Step 3: Result
$\Delta U=6\times 6\times 15=540$ cal, option (D).

Final Answer:
The internal energy increases by 540 cal. \[ \boxed{\text{(D) }540\ \text{cal}} \]