Q 11-12-131JEE MainJEE Main 2020 (4 Sep, Shift 1)Easy
A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\ \text{K}$. If $0.05$ mole of the same gas at $400\ \text{K}$ is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to ______.
Numerical value type. Enter your answer.
Answer: 267
Total internal energy is conserved, and $U = n\cdot\tfrac32RT$ for both portions:
$$T = \frac{0.1\times200 + 0.05\times400}{0.15} = \frac{40}{0.15} \approx 267\ \text{K}$$
Solution by Sreeraj P, M.Sc Physics