Answer to Question #156517 in Mechanical Engineering for Rodel

Question

For cretain ideal gas, R = 0.32 KJ/kg_m - K and c_p = 1160 J/kg_m- K. (a) Find c_v and k. (b) If 6 kg_m of this gas undergo a reversible nonflows constant pressure process from V₁ = 2.1 cu. m, p₁ = 0.7 MPaa to a state where T₂ = 830 K, find ▲H, ▲U, and Q and W.

Answer 1

(a) R = C_p - C_v

C_v = C_p - R = 1160 J/kgK - 320 J/kgK = 840 J/kgK

k = C_p / C_v = 1160 / 840 = 1.38

(b) m = 6 kg

p = const

V₁ = 2.1 m³

p = 0.7 MPa = 7 x 10⁵ Pa

T₂ = 830 K

T₁ = pV₁ / mR = (7 x 10⁵ Pa × 2.1 m³) / (6 kg x 320 J/kgK) = 765.6 K

V₂ = T₂mR / p = (830 K × 6 kg x 320 J/kgK) / 7 x 10⁵ Pa = 2.28 m³

Q = ∆H = mC_p(T₂ - T₁) = 6 kg x 1160 J/kgK x (830 K - 765.6 K) = 448 224 J = 448 kJ

∆U = mC_v(T₂ - T₁) = 6 kg x 840 J/kgK x (830 K - 765.6 K) = 324 576 J = 325 kJ

W = p∆V = p x (V₂ - V₁) = 7 x 10⁵ Pa x (2.28 m³ - 2.1 m³) = 126 000 J = 126 kJ