Question 920: Thermodynamics & KTG

Question

An ideal gas at $$27^{\circ} \mathrm{C}$$ is compressed adiabatically to $$(8 / 27)$$ of its original volume. If ratio of specific heats, $$\gamma=5 / 3$$ then the rise in temperature of the gas is

Accepted Answer

For an adiabatic process $$\mathrm{TV}^{\gamma-1}=$$ constant
$$\begin{aligned}
& 	herefore \frac{T_2}{T_1}=\left(\frac{V_1}{V_2}ight)^{\gamma-1}=\left(\frac{27}{8}ight)^{\frac{5}{3}-1}=\left(\frac{27}{8}ight)^{\frac{2}{3}}=\frac{9}{4} \
& 	herefore T_2=\frac{4}{9} \cdot T_1=\frac{4}{9} 	imes 300=675 \mathrm{~K} \
& 	herefore T_2-T_1=675-300=375 \mathrm{~K}
\end{aligned}$$

Answer

500 K

Answer

125 K

Answer

250 K

Answer

375 K

Thermodynamics & KTG

An ideal gas at $27^{\circ} \mathrm{C} is compressed adiabatically to (8 / 27) of its original volume. If ratio of specific heats, \gamma=5 / 3$ then the rise in temperature of the gas is

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