Question 941: Thermodynamics & KTG

Question

The relation obeyed by a perfect gas during an adiabatic process is $$\mathrm{PV}^{3 / 2}$$. The initial temperature of the gas is '$$\mathrm{T}$$'. When the gas is compressed to half of its Initial volume, the final temperature of the gas is

Accepted Answer

Relation between $$\mathrm{P}$$ and $$\mathrm{V}$$ is given as
$$\mathrm{PV}^{3 / 2}=	ext { constant }$$
For adiabatic process, $$\mathrm{PV}^\gamma=$$ constant
$$	herefore \gamma=\frac{3}{2}$$
The relation between $$\mathrm{T}$$ and $$\mathrm{V}$$ is given by
$$\begin{aligned}
& \mathrm{TV}^{\gamma-1}=	ext { constant } \
	herefore & \mathrm{T}_1 \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_0 \mathrm{~V}_0^{\gamma-1} \
	herefore & \mathrm{T}_1 \mathrm{~V}_1^{1 / 2}=\mathrm{T}_0 \mathrm{~V}_0^{1 / 2} \
	herefore & \frac{\mathrm{T}_2}{\mathrm{~T}_1}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}ight)^{1 / 2}=2^{1 / 2}=\sqrt{2} \
	herefore & \mathrm{T}_2=\sqrt{2} \mathrm{~T}_1=\sqrt{2} \mathrm{~T}
\end{aligned}$$

Answer

$$2 \sqrt{2} \mathrm{~T}$$

Answer

$$4 \mathrm{~T}$$

Answer

$$\sqrt{2} \mathrm{~T}$$

Answer

$$2 \mathrm{~T}$$

Thermodynamics & KTG

The relation obeyed by a perfect gas during an adiabatic process is $\mathrm{PV}^{3 / 2}. The initial temperature of the gas is '\mathrm{T}$'. When the gas is compressed to half of its Initial volume, the final temperature of the gas is

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