Question

(Ideal, reversible, adiabatic flow compressor) Methane is compressed from 298 K and 1 atm to 4 atm. What is the work required per mole? And, what is the final temperature?

Answer 1

Specific heat capacity at constant pressure Cp = 35.5 J/mol·K

Specific heat capacity at constant volume Cv = 27.1 J/mol·K

Specific heat capacity ratio n = Cp/Cv = 35.5/27.1 = 1.31

Initial temperature T1 = 298 K

Initial pressure P1 = 1 atm

Final pressure P2 = 4 atm

Final temperature T2 =?

T2/T1 = (P2/P1)^(n-1/n)

T2/298 = (4/1)^(1.31-1/1.31)

T2/298 = 1.388

T2 = 413.68 K

Work done in reversible adiabatic process

W = R(T2 - T1) / (n - 1)

= 8.314 J/mol·K x (413.68 - 298) K / (1.31 - 1)

= 961.7635 / 0.31

= 3102.46 J/mol