Question 291: Thermodynamics & KTG

Question

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{\mathrm{Cp}}{\mathrm{Cv}}$ will be.

Accepted Answer

Let $\gamma$ be the ratio of $\frac{C_{p}}{C_{v}}$
Then for adiabatic process
$$
\begin{aligned}
& P V^{\gamma}=	ext { Constant } \\
& \Rightarrow \frac{P_{i}}{P_{f}}=\left(\frac{V_{f}}{V_{i}}ight)^{\gamma} \\
& \Rightarrow \frac{81}{16}=\left(\frac{27}{8}ight)^{\gamma} \\
& \Rightarrow \gamma=\frac{4}{3}
\end{aligned}
$$

Answer

$\frac{3}{1}$

Answer

$\frac{4}{3}$

Answer

$\frac{1}{2}$

Answer

$\frac{3}{2}$

Thermodynamics & KTG

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is \frac{16}{81}. Then the ratio of \frac{\mathrm{Cp}}{\mathrm{Cv}} will be.

Choose the correct answer: