Question

A gas is compressed from 120 kPa and 15oC to 800 kPa. Calculate the final temperature when

the process is

i. Isothermal (n=1)

ii. Polytropic (n=1.3)

iii Adiabatic (γ=1.4)

iv. Polytropic (n= 1.5)

Answer 1

Solution.

i. $T_2=T_1=15^oC;$

ii. $T2 = T1 (p2 / p1)^{ 1-1/n} = 288(800/120)^{0.231} = 446 K= 173^oC;$

III.$T_2 = T_1 (p_2 / p_1)^{ 1-1/γ} = 288(800/120)^{0.286} = 495 K= 222^oC;$

iv.$T_2 = T_1 (p_2 / p_1)^{ 1-1/n }= 288(800/120)^{0.333} = 541 K =269^oC;$

Answer: $i. T_2=15^oC;$

$ii. T_2=173^oC;$

$iii. T_2=222^oC;$

$iv. T_2=269^oC;$