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),

A. The final pressure is 0.776bar

Explanation:

To obtain the final pressure, we use the formula:

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

P1 = 4bar = 400kPa

T1 = 438K

T2 = 300K

Polytropic index, n= 1.3

So therefore,

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

P2 = 4(300/438)^1.3/0.3

P2= 4(300/438)^4.333

P2 = 4 * 0.19400

P2 = 0.776bar.

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