The volume of an ideal gas (γ = 1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

Question

The volume of an ideal gas \((\gamma=1.5)\) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

(1) \( \frac{4}{5}\)

(2) \(\frac{16}{25}\)

(3) \(\frac{8}{5 \sqrt{5}}\)

(4) \(\frac{2}{\sqrt{5}}\)   

Answer 1

Correct option is : (3) \(\frac{8}{5 \sqrt{5}}\)  

For Adiabatic process

\( \begin{aligned} & P_{i} V_{i}=P_{f} V_{f}^{\gamma} \end{aligned} \) 

\( \begin{aligned}\ P_{i}(5)^{1.5}=P_{f}(4)^{1.5} \\ \end{aligned}\) 

\( \begin{aligned}\frac{P_{i}}{P_{f}}=\left(\frac{4}{5}\right)^{\frac{3}{2}}=\frac{4}{5} \cdot\left(\frac{4}{5}\right)^{\frac{1}{2}} \Rightarrow \frac{8}{5 \sqrt{5}} \end{aligned}\)