Question 235: Thermodynamics & KTG

Question

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $$\gamma=3 / 2$$. The work done by the gas in the process is:
$$(\mu=1 	ext { mole })$$

Accepted Answer

$$\begin{aligned}
& w=\frac{-n R}{\gamma-1}(\Delta T) \
&=\frac{-R}{1 / 2}\left(\frac{T}{\sqrt{2}}-Tight) \
&=2 R\left(\frac{\sqrt{2} T-T}{\sqrt{2}}ight) \
&=R T(2-\sqrt{2}) \
& 	herefore \quad T V_\gamma^{-1}=	ext { cons. } \
& T V_\gamma^{-1}=T_f(2 V)^{\gamma-1} \
& T_f=\frac{T}{\sqrt{2}}
\end{aligned}$$

Answer

$$R T[2 \sqrt{2}-1]$$

Answer

$$R T[2-\sqrt{2}]$$

Answer

$$R T[1-2 \sqrt{2}]$$

Answer

$$R T[\sqrt{2}-2]$$

Thermodynamics & KTG

A sample of gas at temperature $T is adiabatically expanded to double its volume. Adiabatic constant for the gas is \gamma=3 / 2. The work done by the gas in the process is: (\mu=1 \text { mole })

Choose the correct answer: