Question 888: Thermodynamics & KTG

Question

A monoatomic gas $$\left(\gamma=\frac{5}{3}\right)$$ initially at $$27^{\circ} \mathrm{C}$$ having volume '$$\mathrm{V}$$' is suddenly compressed to one-eighth of its original volume $$\left(\frac{\mathrm{V}}{8}\right)$$. After the compression its temperature becomes

Accepted Answer

For adiabatic charge, $$\mathrm{PV}^\gamma=$$ constant as well as $$\mathrm{TV}^{\gamma-1}=$$ constant and for a monoatomic gas $$\gamma=\frac{5}{3}$$
$$\begin{aligned}
& 	herefore \mathrm{T}_1 \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_2 \mathrm{~V}_2^{\gamma-1} \
& 	herefore \frac{\mathrm{T}_2}{\mathrm{~T}_1}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}ight)^{\gamma-1}=\left(\frac{\mathrm{V}}{\mathrm{V} / 8}ight)^{5 / 3-1}
\end{aligned}$$
$$\begin{aligned}
& 	herefore \frac{\mathrm{T}_2}{\mathrm{~T}_1}=(8)^{2 / 3}=\left(2^3ight)^{2 / 3}=4 \
& 	herefore \mathrm{T}_2=4 \mathrm{~T}_1 	ext { but } \mathrm{T}_1=273+27=300 \mathrm{~K} \
& 	herefore \mathrm{T}_2=4 	imes 300=1200 \mathrm{~K}
\end{aligned}$$

Answer

580 K

Answer

1200 K

Answer

1160 K

Answer

927 K

Thermodynamics & KTG

A monoatomic gas $\left(\gamma=\frac{5}{3}\right) initially at 27^{\circ} \mathrm{C} having volume '\mathrm{V}' is suddenly compressed to one-eighth of its original volume \left(\frac{\mathrm{V}}{8}\right)$. After the compression its temperature becomes

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