Question 860: Thermodynamics & KTG

Question

A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$$ is its initial volume. The initial temperature of the gas is $$T_i$$ in Kelvin and the final temperature is '$$x T_i$$'. The value of '$$x$$' is

Accepted Answer

For adiabatic process: $$\mathrm{TV}^{\gamma-1}=$$ Constant
$$	herefore$$ Initially:
$$\mathrm{T}_{\mathrm{i}} \mathrm{V}^{\frac{7}{5}-1}=	ext { Constant }$$
$$	herefore \quad$$ Final condition:
$$\mathrm{xT}_{\mathrm{f}} \mathrm{V}^{\frac{7}{5}-1}=	ext { Constant }$$
So,
$$\begin{aligned}
& T_i V^{\frac{7}{5}-1}=x T_f V^{\frac{7}{5}-1} \
& T^{\frac{2}{5}}=x T\left(\frac{V}{32}ight)^{\frac{2}{5}} \
& x=4
\end{aligned}$$

Answer

5

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4

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3

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2

Thermodynamics & KTG

A diatomic gas $\left(\gamma=\frac{7}{5}\right) is compressed adiabatically to volume \frac{V_i}{32} where V_i is its initial volume. The initial temperature of the gas is T_i in Kelvin and the final temperature is 'x T_i'. The value of 'x$' is

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