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Topic: Equation of state of a perfect gas, work done on compressing a gas· Kinetic Theory of Gases

A container has two chambers of volumes V_1 = 2 litres and V_2 = 3 litres separated by a partition made of a thermal insulator. The chambers contains n_1 = 5 and n_2 = 4 moles of ideal gas at pressures p_1 = 1 atm and p_2 = 2 atm, respectively. When…

A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contains \(n_1 = 5\) and \(n_2 = 4\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :

1. 1.3 atm

2. 1.6 atm

3. 1.4 atm

4. 1.8 atm

1 answer

Best answer

Answer: 2. 1.6 atm

Key idea: no heat or work leaves the container, so the total internal energy is conserved. For the same gas, this gives \(n_1T_1+n_2T_2=(n_1+n_2)T\), which leads to \(p(V_1+V_2)=p_1V_1+p_2V_2\) (since \(nRT=pV\) for each part).

$$p=\frac{p_1V_1+p_2V_2}{V_1+V_2}=\frac{1\times2+2\times3}{2+3}=\frac85=1.6\ \mathrm{atm}$$
Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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