Question

Dry air at `15^0 C` and 10 atm is suddenly released at atmospheric pressure. Find the final temperature of the air `[C_p / C_v = 1.41]`.

Answer 1

As the air is suddenly released, it does not get
time to exchange heat with the surrounding. Thus the
process is adiabatic. Assuming the process to be reversible,
`T^gamma / P gamma^(-1)` = constant
or, `T_1^gamma / P_1 gamma^(-1)` = T_2 gamma / P_2 gamma (-1)`
or `(T_2 / T_1)gamma = ( P_2 / P_1) gamaa ^(-1)`
or, `T_2 = T_1 (P_2/ P_1)gamma^(-1)/gamma.