Question

Argon is compressed in a polytropic process with n=1.2 from 120 kPa and 10 °C to 800 kPa in a piston cylinder device. Determine: (a) The work produced and, (b) Heat transferred during this compression process, in KJ/kg.

Answer 1

Answer:

a. W = - 108.89 kJ/kg

b. q =  - 75.846 kJ/kg

Given:

n = 1.2

Pressure, P = 120 kPa

Temperature, T = $10^{\circ}$ = 283 K

Pressure, P' = 800 kPa

Solution:

(a) Work Produced:

Now, using the relation:

W = $\frac{RT}{1 - n}[(\frac{P'}{P})^(1 - \frac{1}{n}) - 1]$

where

R = Rydberg's constant

Now,

W = $\frac{283\times0.208}{1 - 1.2}[(\frac{800}{120})^(1 - \frac{1}{1.2}) - 1]$

W = $\frac{283\times0.208}{- 0.2}[(6.67)^(0.16) - 1] = - 108.89 kJ/kg$

Now,

$\frac{T'}{T}= (\frac{P'}{P})^{1 - \frac{1}{n}}$

$T'= T(\frac{800}{120})^{1 - \frac{1}{1.2}}$

$T'= 1.37\times 283 = 388.48 K$

(b) Heat tranferred, q = $C_{v}(T' - T) + W$

q = $0.3122(388.84 - 283) - 108.89 = - 75.846 kJ/kg$