Question

A 1-m³ insulated, rigid tank contains air at 800 kPa, 25°C. A valve on the tank is opened, and the pressure inside quickly drops to 150 kPa, at which point the valve is closed. Assuming that the air remaining inside has undergone a reversible adiabatic expansion, calculate the mass withdrawn during the process. 

Answer 1

C.V.: Air remaining inside tank, m₂. 

Cont.Eq.: m₂ = m ;

Energy Eq.  m(u₂ − u₁) = ₁Q₂ − ₁W₂ 

Entropy Eq   m(s₂ − s₁) = ∫ dQ/T + ₁S_{2 gen} 

Process: adiabatic ₁Q₂ = 0 and reversible ₁S_{2 gen} =  0

Entropy eq. then gives s₂ = s₁ and ideal gas gives the relation