Air at 257°C and 400 kPa is contained in a piston cylinder device. The air expands adiabatically until the pressure is 100 kPa. Determine the mass of air needed to produce maximum work of 1000 kJ. Assume air has constant specific heats evaluated at 300 K.

The mass of the air to produce the work

m = 8.034 kg

Explanation:

Using the equation of work and energy in the system can find the mass of air needed to produce that work

T₁ = 273 °K + 257 ° C

T₁ = 530 °K, c₁ = 0.718

Eₙ - E₀ = Δ E system

- W₀ = ΔU

- W₀ = m * (u₂ - u₁)

T₂ = T₁ * (P₂ / P₁) ⁰²⁸⁶

T₂ = 530 ° K * (100 kPa / 400 kPa) ⁰²⁸⁶

T₂ = 356.66 ° K

W₀ = m * c₁ * (T₁ - T₂)

m = W₀ / [ c₁ * (T₁ - T₂) ]

m = 1000 kJ / 0.718 * (530 - 356.66) ° K

m = 8.034 kg