Question:
A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.
A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.
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No heat or work is exchanged with the surroundings, so the total internal energy \(U = nC_vT\) is conserved: \(n_1T_1 + n_2T_2 = (n_1+n_2)T\).
Updated On: Nov 5, 2026
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Correct Answer: 267
Solution and Explanation
The vessel is closed and insulated from the surroundings (no heat or work exchange), so the total internal energy is conserved. For a monoatomic ideal gas \(U = \frac{3}{2}nRT\).
\(\frac{3}{2}R(0.1)(200) + \frac{3}{2}R(0.05)(400) = \frac{3}{2}R(0.15)T\).
\(20 + 20 = 0.15\,T\) so \(T = \frac{40}{0.15} = 266.67\ \mathrm{K} \approx 267\ \mathrm{K}\).
Answer: 267
\(\frac{3}{2}R(0.1)(200) + \frac{3}{2}R(0.05)(400) = \frac{3}{2}R(0.15)T\).
\(20 + 20 = 0.15\,T\) so \(T = \frac{40}{0.15} = 266.67\ \mathrm{K} \approx 267\ \mathrm{K}\).
Answer: 267
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