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 adiabaticall…

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

γ = 1.5; γ

is the ratio of specific heats at constant pressure and at constant volume)

Accepted Answer

Correct answer: A. (a) To determine the change in temperature when a gas is adiabatically compressed, we are given the following initial conditions: Initial volume, V_1=800 cm^3 Final volume, V_2=200 cm^3 Initial temperature, T_1=27^ C=300 K Adiabatic index (ratio of specific heats) =1.5 In an adiabatic process, the relationship between temperature and volume is given by the equation: TV^ -1= constant Applying this to the initial and final states: 300 (800 )^0.5=T_2 (200 )^0.5 Solving for the final temperature T_2 : T_2=300 ( 800200 )^0.5=300 (4 )^0.5T_2=300 2=600 K Thus, the change in temperature is: T=T_2-T_1=600 K-300 K=300 K Therefore, when the gas is adiabatically compressed, the temperature increases by 300 K.

Solution

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