Question

#4 A system containing 2.50 moles of an ideal gas for which = 20.79 JK^-1mol^-1 is taken through the following cycles: (1) an isobaric expansion (P₁ = 16.6 bar) from V₁ = 1.00 L to V₂ = 25.0 L; (2) an isochoric cooling from T₂ to the original temperature, T₁; followed by (3) an isothermal compression (at temperature T₁) to the original pressure P₁ and volume V₁.

A. Represent the above processes on a P-V diagram

B. Calculate q, w, ΔU and ΔH for each segment and for the whole cycle.

Answer 1

a)

b)

For Isobaric Expansion,

P = 16.6 bar

V₁ = 1 L

V₂ = 25 L

T₁ = P₁V₁ / nR = 80.877 K

T₂ = P₂V₂ / nR = 2021.92 K

w = - P (V₂ - V₁)

w = - 16.6 ( 25 - 1 ) = - 398.4 J

U = nC_vT = 2.5 x 20.79 x (2021.92 - 80.877)

U = 100885.943 J

q = U - w = 100885.943 + 398.4 = 101284.34 J

H = nC_pT = 2.5 x (20.79+8.314) x (2021.92 - 80.877)

H = 141230.289 J

For Isochoric cooling,

V = 0 = w

q = U = nC_vT = 2.5 x 20.79 x (80.877 - 2021.92)

q = U = -100885.943 J

H = nC_pT = 2.5 x (20.79+8.314) x (80.877 - 2021.92)

H = -141230.289 J

For Isothermal Compression,

T = 0 = U = H

q = w = nRTln(V₂/V₁)

q = w = (2.5)(8.314)(80.877)ln(1/25)

q = w = 5411.022 J