Question

An ideal gas expands according to the law $P^2V$ = constant. On expansion, the temperature

• A. decreases
• B. increases
• C. remains constant
• D. None of these

Answer 1

Answer: (B)

increases

Answer 2

Given the law $P^2V = K$ and the ideal gas law $PV = nRT$. Squaring the ideal gas law gives $P^2V^2 = n^2R^2T^2$. From $P^2V = K$, we have $P^2 = K/V$. Substituting this into the squared ideal gas law: $(K/V)V^2 = n^2R^2T^2$, which simplifies to $KV = n^2R^2T^2$. This shows $T^2 \propto V$, or $T \propto \sqrt{V}$. During expansion, $V$ increases, and therefore $T$ increases.