Argon is compressed in a polytropic process with n = 1.2 from 100 kPa and 30°C to 1200 kPa in a piston–cylinder device. Determine the final temperature of argon.

181 °C

Explanation:

Initial pressure = 100 kPa

Initial temperature = 30 °C = 30 + 273 K = 303 K

Final pressure = 1200 kPa

Final temperature = ?

n = 1.2

For a polytropic process, we use the relationship

(/ ) = (/)^γ

where γ = (n-1)/n

γ = (1.2-1)/1.2 = 0.1667

substituting into the equation, we have

(/303) = (1200/100)^0.1667

/303 = 12^0.1667

/303 = 1.513

= 300 x 1.513 = 453.9 K

==> 453.9 - 273 = 180.9 ≅ 181 °C

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