Question

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of \(800 \ cm^3\) and temperature \(27 ^\circ C\). The change in temperature when the gas is adiabatically compressed to \(200 \ cm^3\) is :

(Take \(\gamma = 1.5 : \gamma\) is the ratio of specific heats at constant pressure and at constant volume)

(1) 327 K

(2) 600 k

(3) 522 K

(4) 300 K

Answer 1

Correct option is : (4) 300 K

Being adiabatic process \(PV^ \gamma = \) constant, where \(\gamma = 1.5\) and also \(TV^{\gamma-1} = \) constant

\(300 \{800\}^{0.5} = T\{200\} ^{0.5}\)

\(T = 300 \times 2 = 600 K\)

\(\Delta = 600 - 300 = 300 K\)