Question

Derive the entropy change in the isothermal expansion of an ideal gas.

Answer 1

let v1, p1 be the initial volume and pressure of gas

v2, p2 are the final volume and pressure of gas

we know from the first law of thermodynamics, Q= W + dU

dU= change in internal energy and for an isothermal process, dU=0

so Q = W

where w= work done in an isothermal process

W=n RT ln (V2/V1)

n= number of moles, R = universal gas constant, T= temperature of gas

also for an isothermal process, P1/P2= V2/V1

so W= n RT ln (P1/P2)

so Q= n RT ln (V2/V1) =n RT ln (P1/P2)

now change in entropy= S= Q/T

S=[n RT ln (V2/V1) ]/T

S= n R ln (V2/V1) or n R ln (P1/P2)