Question

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.

Answer 1

Answer:

181 °C

Explanation:

Initial pressure $P_{1}$ = 100 kPa

Initial temperature $T_{1}$ = 30 °C = 30 + 273 K = 303 K

Final pressure $P_{2}$ = 1200 kPa

Final temperature $T_{2}$ = ?

n = 1.2

For a polytropic process, we use the relationship

($T_{2}$/$T_{1}$ ) = ($P_{2}$/$P_{1}$)^γ

where γ = (n-1)/n

γ = (1.2-1)/1.2 = 0.1667

substituting into the equation, we have

($T_{2}$/303) = (1200/100)^0.1667

$T_{2}$/303 = 12^0.1667

$T_{2}$/303 = 1.513

$T_{2}$ = 300 x 1.513 = 453.9 K

==> 453.9 - 273 = 180.9 ≅ 181 °C