One mole of a gas at 27^(@)C and 3 atmospheric pressure is compressed to 1/3 of its volume (a) slowly (b) suddenly. What is the resulting temperature ? gamma =1 .4.

One mole of a gas at 27^(@)C and 3 atmospheric pressure is compressed

1.	One mole of a gas at 27^(@)C and 3 atmospheric pressure is compressed to 1/3 of its volume (a) slowly (b) suddenly. What is the resulting temperature ? gamma =1 .4.
Answer» Solution :(a) Slowly, i.e., isothermal, PV =a constatn at constatn temperature So final temperature `= 27 ^(@)C= 300 K` (b) Suddenly i.e., adiabatic `T_(1)V_(1) ^( gamma -1) = T_(2)V_(2) ^( gamma -1) , T_(1) = 27 + 273 = 300 KV _(1) = V _(1)` `V_(2) = 1//3 V_(1) T_(2) = ?` `T_(2) = T_(1) ((V_(1))/( V _(2))) ^( gamma -1) = 300 ((V _(1))/(V _(1) //3)) ^( 1. 4 - gamma)= 300 XX (3) ^( 0.4)` `log T_(2) = log 300 + 0.4 xx log 3` `= 2. 6679 T_(2) = ` Antilog of `2. 6679` `T_(2) = 465.5K`