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 2 7 ∘ C . The change in temperature when the gas is adiabatical

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 $2 7^{\circ} C$ . 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)

TestHub · Accepted Answer

​ V 1 ​ = 800 cm 3 V 2 ​ = 200 cm 3 T 1 ​ = 300 K ​ for adiabatic ​ TV γ − 1 = const. ( 300 ) ( 800 ) 1.5 − 1 = T 2 ​ ( 200 ) 1.5 − 1 T 2 ​ = 300 [ 200 800 ​ ] 0.5 = 300 × ( 2 2 ) 1/2 T 2 ​ = 600 K Δ T = 600 − 300 = 300 K ​

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