Discussion
One litre of an ideal gas at a pressure of 50 pascal is suddenly compressed to half its original volume. The final pressure of the gas in pascal is ( γ = 1.5)
Answer: D
The final pressure is \(100\sqrt{2}\) Pa.
'Suddenly compressed' means adiabatic, so \(PV^{\gamma}\) is constant:
\[ \begin{aligned} P_{2} &= P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma} = 50 \times 2^{1.5} \\ &= 50 \times 2\sqrt{2} = 100\sqrt{2} \end{aligned} \]
100 Pa is the isothermal answer (Boyle's law, \(\gamma\) taken as 1), and \(50\sqrt{2}\) uses the power 0.5.
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