Question

An ideal gas is expanded from 10 bar to 1.0 bar at constant temperature. Calculate deltaU, deltaH, and deltaS. C_P = 5/2 R.

Answer 1

In an isothermal expansion, heat is allowed to flow into or out of the system so that temperature remains constant throughout the process of expansion. Since, for an ideal gas, the internal energy, ΔU, depends only on temperature, if follows that at constant temperature, the internal energy of the gas remains constant, that is ΔU = 0.

Calculation of ΔH can be done according to the following equation:

ΔH = ΔU + Δ(PV)

ΔH = ΔU + Δ(nRT)

Since for isothermal process, ΔU and ΔT are zero respectively, hence, ΔH = 0

ΔS = 2.303nRlog [P₁/P₂]                                     ( n=1, for an ideal gas and C_P =5/2 R indicates monoatomic gas)

ΔS = 2.303x 1 x(8.314 J/K mol )x log [10 bar/1.0 bar]

ΔS = 2.303 x 1 mol x (8.314 J/K mol ) x 1 = 19.14 J/K