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Topic: First law of thermodynamics· Thermodynamics

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius r_A and r_B, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B…

Two gases \(A\) and \(B\) are filled at the same pressure in separate cylinders with movable pistons of radius \(r_A\) and \(r_B\), respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas \(A\) and \(B\) are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio \(r_A/r_B\) is equal to

1. \(\frac{4}{3}\)

2. \(\frac{3}{4}\)

3. \(\frac{2}{\sqrt3}\)

4. \(\frac{\sqrt3}{2}\)

1 answer

Best answer

Answer: 2. \(\frac{3}{4}\)

Key idea: at constant pressure, \(Q=\Delta U+W\) with \(W=p\Delta V\).

The heat supplied and \(\Delta U\) are the same for both gases, so \(W\) is equal. With the same pressure, \(\Delta V\) is equal:

$$\pi r_A^2h_A=\pi r_B^2h_B\Rightarrow\left(\frac{r_A}{r_B}\right)^2=\frac{9}{16}\Rightarrow\frac{r_A}{r_B}=\frac34$$
Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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