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°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)

• A. 327 K
• B. 600 K
• C. 522 K
• D. 300 K

Hint:

Use the adiabatic process equation to relate the initial and final temperatures and volumes. Remember to use consistent units for volume.

Answer 1

The Correct Option is D

\( V_1 = 800 cm^3 \) \( V_2 = 200 cm^3 \) \( T_1 = 300 \) 

K For adiabatic: \( TV^{\gamma - 1} = \) constant. 

\( T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1} \) \( (300) (800)^{1.5 - 1} = T_2 (200)^{1.5 - 1} \) \( T_2 = 300 \left( \frac{800}{200} \right)^{0.5} \) \( T_2 = 300 (4)^{1/2} \) 

\( T_2 = 600 \) K \( \Delta T = 600 - 300 = 300 \) K