Question

Initially a sample of ideal gas at 323 K occupies 1.67 L at 4.95 atm. The gas is allowed to expand to 7.33L by two pathways: (a) isothermal, reversible expansion; (b) isothermal irreversible free expansion. Calculate Delta S_tot, Delta S and Delta S_surr for each pathway

Answer 1

We have P = 4.95 atm, T= 323 K, V₁ = 1.67 L & V₂ = 7.33 L

(a) Isothermal Reversible Expansion

ΔS (system) = R ln V₂/V₁ = Q(rev)/T = 8.314*ln(7.33/1.67) = 12.3 J/K

Since process is reversible ΔS (Total) = 0.

So ΔS (surr) = - ΔS (system) = -12.3 J/K

(b) Isothermal irreversible free expansion

Free expansion - the gas expands into vaccum for this process , we have w = 0
Δ U = 0 as it is a constant temperature process
so from first law ΔU = w + q
0 = 0 + q
that means q = 0

since entropy is a state function the entropy change of a system in going from volume V₁ to V₂ by any path will be same as that of a reversible change :
therefore, ΔS (system) = R ln V₂/V₁
since no heat is supplied by surroundings the entropy change of latter will be zero
ΔS (surroundings) = 0

so ΔS (total) = ΔS (system) + ΔS (surroundings) = R ln V₂/V₁ + 0 = R ln V₂/V₁ = 12.3 J/K