A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 is: (Take = 1.5 : is the ratio of spec

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Solution

Q.
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°C. The change in temperature when the gas is adiabatically compressed to 200 ${cm}^{3}$ is:

(Take $γ$ = 1.5 : $γ$ is the ratio of specific heats at constant pressure and at constant volume) [2025]

1 327 K

2 600 K

3 522 K

4 300 K

Ans.
(4)

$V_{1} = 800 {cm}^{3}, V_{2} = 200 {cm}^{3}, T_{1} = 300 K$

for adiabatic process, $T V^{γ - 1}$ = const.

$(300) {(800)}^{1.5 - 1} = T_{2} {(200)}^{1.5 - 1}$

$T_{2} = 300 {[\frac{800}{200}]}^{0.5} = 300 \times {(2^{2})}^{1 / 2}$

$T_{2} = 600 K$

$△ T = 600 - 300 = 300 K$

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