First slide

Thermodynamic processes

Question

A gas at NTP is suddenly compressed to one-fourth of its original volume. If $γ$ is supposed to be $\frac{3}{2}$ , then the final pressure is

Moderate

A

4 atmosphere
B

$\frac{3}{2}$ atmosphere
C

8 atmosphere
D

$\frac{1}{4}$ atmosphere

Solution

$\begin{array}{l} {PV}^{γ} = constant \Rightarrow \frac{P_{2}}{P_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ} \Rightarrow \frac{P_{2}}{1} = {(\frac{V_{1}}{V_{1} / 4})}^{3 / 2} = 8 \\ \Rightarrow P_{2} = 8 atm \end{array}$

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