Question

An ideal gas is taken from an initial state i to a final state f in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by the gas?

Answer 1

Let:-

P₁ = Initial pressure

P₂ = Final pressure

T₁ = Absolute initial temperature

T₂ = Absolute final temperature

Given :-

\[\frac{P_1}{T_1} = \frac{P_2}{T_2}\]

Using the ideal gas equation, we get

PV = nRT

If n is the number of moles of the gas and R is the universal gas constant, then

\[\frac{P_1}{T_1} = \frac{nR}{V_1}\text{ and }\frac{P_2}{T_2} = \frac{nR}{V_2}\]

\[ \Rightarrow  V_1  =  V_2 .........\left[ \because \frac{P_1}{T_1} = \frac{P_2}{T_2} \right]\]

\[ \Rightarrow  ∆ V =  V_2  -  V_1  = 0\]

Thus, Work done by gas = P∆V = 0