Answer to Question #156517 in Mechanical Engineering for Rodel

Question #156517

For cretain ideal gas, R = 0.32 KJ/kgm - K and cp = 1160 J/kgm- K. (a) Find cv and k. (b) If 6 kgm 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.


1
Expert's answer
2021-01-25T04:09:39-0500

(a) R = Cp - Cv

Cv = Cp - R = 1160 J/kgK - 320 J/kgK = 840 J/kgK

k = Cp / Cv = 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 = mCp(T2 - T1) = 6 kg x 1160 J/kgK x (830 K - 765.6 K) = 448 224 J = 448 kJ

∆U = mCv(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


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