Question

Calculate q, w, ΔU and ΔH for the reversible adiabatic compression of 0.2 mole
of an ideal gas (diatomic) at 27 C from a volume 1 dm3
to a volume of 0.25
dm3

Answer 1

Q = 0

C_v = 5R/2 = 20.79 J/(mol*K)

γ = 1.4

T₁ = 27+273 = 300 K

T₁*V₁^γ-1 = T₂*V₂^γ-1

T₂ = 300*1^0.4/0.25^0.4 = 522 K

W = - n*C_v*$\Delta$T = -0.2*20.79*(522-300) = -923 J

ΔU = -W = 923 J

C_p = 7R/2 = 29.10 J/(mol*K)

ΔH = n*C_p*$\Delta$T = 0.2*29.10*(522-300) = 1292 J