Answer:
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