(30 Points) A piston–cylinder arrangement containing Nitrogen (N2), initially at 4 bar and 438 K, undergoes an expansion to a final temperature of 300 K, during which the pressure–volume relationship is pV1.3 = constant. Assuming the ideal gas model for the N2, determine: (a) the final pressure (bar), (b) the work (kJ), and (c) the heat transfer in kJ/k

A. Final pressure P2

P2/P1 = (T2/T1)^n/n-1

P1 = 4bar

T1 = 438K

T2 = 300K

Polytropic index, n, = 1.3

P2 = 4 (300/438)^1.3/1.3-1

P2 = 4 (300/438)^4.333

P2 = 4 * 0.19400

P2 = 0.776bar.

B. The work done is;

W = mR/ n-1 (T1 -T2)

Where, R = 0.1889kJ/kg.K, m = 1

W = 1 * 0.1889/ 1.3-1 * (438-300)

W = 86.89kJ/kg.

C. The heat transfer, Q

Q = W + ΔU

Q = W + mCv(T2-T1), where Cv of nitrogen is 0.743kj/kgk

Q = 86.89 + 1 * 0.743 (300-438)

Q = 86.89 + (-102.534)

Q = -15.644kJ/K

Q = 15.64kJ/K

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