One mole of an ideal gas at temperature T1 expands according to the law (P/V) = constant. Find the work done when the final temperature becomes T2 :
Answer & explanation
Correct answer: option 2
W = \(\int_{V_1}^{V_2} P dV\)
= \(\int_{V_1}^{V_2} KV dV\) ... (\(\frac{P}{V} = constant = K\))
\(\Rightarrow W = \frac{1}{2} K (V_2^2 - V_1^2)\)
PV = RT
But, P = KV
KV2 = RT
\(\Rightarrow K (V_2^2 - V_1^2) = R(T_2 - T_1)\)
\(\Rightarrow W = \frac{R}{2}(T_2 - T_1)\)