Question 9
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:
Solution
For an adiabatic process: $$PV^{\gamma} = \text{constant}$$.
$$P_1 V_1^{\gamma} = P_2 V_2^{\gamma}$$
$$\frac{P_1}{P_2} = \left(\frac{V_2}{V_1}\right)^{\gamma} = \left(\frac{4}{5}\right)^{3/2}$$
$$= \frac{4^{3/2}}{5^{3/2}} = \frac{8}{5\sqrt{5}}$$
The correct answer is Option 3: $$\frac{8}{5\sqrt{5}}$$.
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