Question 189: Thermodynamics & KTG

Question

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is:
(Take $\gamma=1.5 ; \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

Accepted Answer

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

Answer

300 K

Answer

600 K

Answer

327 K

Answer

522 K

Thermodynamics & KTG

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