Question

One mole of an ideal gas expands isothermally to five times its initial volume.
Calculate the entropy change in terms of R, the gas constant.

Answer 1

The process in which there is no change in temperature is known as isothermal process. Entropy changes from S₁ to S₂ when gas absorbs heat during expansion. The heat taken by gas is given by area under the curve which represents work done during expansion.
Q=W
but, Q=T(S₂-S₁)
and W=P₁V₁ln(V₂/V₁) = RTln(V₂/V₁)
so according to the question;
V₂=5V & V₁=V
so we have a formula fro above equations;
T(S₂-S₁) = RTln(V₂/V₁)
⇒T(S₂-S₁) = RTln(5V/V)
⇒(S₂-S₁) = Rln5
⇒(S₂-S₁) = 1.60944R
Answer: 1.60944R