Anideal gas, which takes up 15.0 dm3 at 250 K and 1 bar is beingisothermally com
ID: 1815627 • Letter: A
Question
Anideal gas, which takes up 15.0 dm3 at 250 K and 1 bar is beingisothermally compressed. To which volume does it have to becompressed to lower its entropy by 5.0 J/K?
Explanation / Answer
dU = Cv*dT = 0 = T*dS - P*dV dT = 0 b/c isothermal => Internal energy does notchange T*dS = P*dV dS = (P/T)*dV = (nR/V)*dV S = nR*ln(Vf/Vi) Vf/Vi = exp(S/nR) Vf = Vi*exp(S/nR) n = PV/(RT) = (1 bar* 15 dm3)/(0.0821 dm3*atm/mol/K *250K) * ( 1e5 Pa/ 1bar) * ( 1 atm/101325 Pa) n = 0.721259391 moles Vf = 15 dm3 * exp(-5 J/K / [0.7213 mol * 8.314 J/mol/K] ) Vf = 6.51615481 dm3 Vf = 6.5 dm3