Question

2.25 moles of an ideal gas with Cv,m = 5R/2 are transformed irreversibly from an intital state T=680 K and P= 1.15 bar to a final state T = 298 K and P = 4.75 bar a) Calculate change in internal energy, change in enthalpy, and change in entropy for this process b) Calculate change in internal energy, change in enthalpy, and change in entropy if this process was reversible.

Answer 1

n = moles = 2.25 ,R = universal gas constant = 8.314 x 10^-3 kJ/mol K

A)

ΔU = n Cv ΔT

         = 2.25 x (5 R / 2 ) x (680-298)

         = 2.25 x ( 5 x 8.314 x 10^-3 / 2 ) x 382

    ΔU    = 17.86 kJ /mol

B )

ΔH = ΔU + n R ΔT

      = 17.86 + 2.25 x 8.314 x 10^-3 x (680-298)

   ΔH = 25 kJ /mol

C)

Cp - Cv = R

Cp -5R/2 =R

Cp = 7R/2 = 7 x 8.314 / 2 = 29.1 J /K

ΔS = n Cp ln (T2/T1) - n R ln (P2/P1)

     = 2.25 x 29.1 ln (680 / 298) - 2.25 x 8.314 x ln (1.15/4.75)

      = 54.0 + 26.53

     = 80.53 J /mol K