Answer to Question #177764 in Chemical Engineering for dady

Question

1 kg of ait at 1 bar 15 degree centridage is compressed reversibly and adiabtically in a pressure of 4 bar.Calculate the final temperature and the work input.

Answer 1

Adiabatic Compression

$\gamma$ for adiabatic air process = 1.4

T₂/T₁ = (P₂/P₁)^{(1.4 - 1)/1.4}

T₂ = (15+273 K)(4 x 10⁵ Pa / 1 x 10⁵ Pa)^0.4/1.4 = 428 K

W = (P₁V₁ - P₂V₂) / ($\gamma$ - 1) = R(T₂ - T₁) / ($\gamma$ - 1)

W = 287 J/kg K (288 - 428 K) x 1 kg / (1.4 - 1) = -100.45 kJ