Answer:
181 °C
Explanation:
Initial pressure [tex]P_{1}[/tex] = 100 kPa
Initial temperature [tex]T_{1}[/tex] = 30 °C = 30 + 273 K = 303 K
Final pressure [tex]P_{2}[/tex] = 1200 kPa
Final temperature [tex]T_{2}[/tex] = ?
n = 1.2
For a polytropic process, we use the relationship
([tex]T_{2}[/tex]/[tex]T_{1}[/tex] ) = ([tex]P_{2}[/tex]/[tex]P_{1}[/tex])^γ
where γ = (n-1)/n
γ = (1.2-1)/1.2 = 0.1667
substituting into the equation, we have
([tex]T_{2}[/tex]/303) = (1200/100)^0.1667
[tex]T_{2}[/tex]/303 = 12^0.1667
[tex]T_{2}[/tex]/303 = 1.513
[tex]T_{2}[/tex] = 300 x 1.513 = 453.9 K
==> 453.9 - 273 = 180.9 ≅ 181 °C
