Air expands adiabatically in a piston–cylinder assembly from an initial state where p1 = 100 lbf/in.2, v1 = 3.704 ft3/lb, and t1 = 1000 °r, to a final state where p2 = 30 lbf/in.2 the process is polytropic with n = 1.4. the change in specific internal energy, in btu/lb, can be expressed in terms of temperature change as (0.171)(t2 - t1). determine the final temperature, in °r. kinetic and potential energy effects can be neglected.

Final temperature is equal to 1291.63°R  

Explanation:

given,

p₁ = 100 lb f/in²,               v₁ = 3.704 ft³/lb,           and T₁ = 1000 °R

p₂ = 30 lb f/in²                 n = 1.4

Δ u = 0.171(T₂ - T₁)

we know for poly tropic process

p vⁿ = constant

p₁ v₁ⁿ = p₂ v₂ⁿ

100 × 3.704¹°⁴ = 30 × v₂¹°⁴

v₂ = 8.753 ft³/lb

work done for poly tropic process

W =

    =

    = 269.525 lbf/in².ft³

W = Btu/lb

   = 49.87 Btu/lb

in the piston cylinder arrangement air is expanding acrobatically

Δ q = Δu + w

Δ u = - w

0.171(T₂ - T₁) = -49.87

0.171(T₁ - T₂) = -49.87

0.171 T₂ = 0.171 × 1000 + 49.87

T₂ = 1291.63 °R

Final temperature is equal to 1291.63°R