A piston-cylinder device contains 0.1 kg of hydrogen gas (PG model: cv=10.18, k = 1.4, R= 4.12 kJ/kg-K) at 1000 kPa and 300 K. The gas undergoes an expansion process and the final conditions are 500 kPa, 270 K. If 10 kJ of heat is transferred into the gas from the surroundings at 300 K, determine (a) the boundary work (Wb), and (b) the entropy generated (Sgen) during the process

(a) 151.84 kJ

(b) 2.922 kJ/K

Explanation:

(a) The parameters given are;

Mass of hydrogen gas, H₂ = 0.1 kg = 100 g

Molar mass of H₂ = 2.016 g/mol

Number of moles of H₂ = 100/2.016 = 49.6 moles

V₁ = mRT/P = 0.1×4.12×300/1000 = 0.1236 m³

P₁/P₂ = (V₂/V₁)^k

V₂ = (P₁/P₂)^(1/k)×V₁ =0.1236 × (1000/500)^(1/1.4) = 0.3262 m³

Boundary work done = (V₂ - V₁)(P₂ + P₁)/2 = (0.3262 - 0.1236)*(500 + 1000)/2 = 151.84 kJ

(b) Entropy generated ΔS = Cv · ㏑(T₂/T₁) + R ·㏑(v₂/v₁)

=10.18 × ㏑(270/300) + 4.12 ·㏑(0.3262/0.1236) = 2.922 kJ/K.

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