A cylinder with a movable piston contains 3 ...

Thermodynamics

Question : 4 of 10

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A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

Solution:

As the gas is completely insulated, the process is adiabatic.

P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma}

\Rightarrow \frac{P_{2}}{P_{1}} = \left(\frac{V_{1}}{V_{2}}\right)^{\gamma}

\frac{P_{2}}{P_{1}} = \left(\frac{V_{1}}{\frac{V_{1}}{2}}\right)^{1.4} \begin{pmatrix} \therefore V_{2}= \frac{1}{2} V_{1} \\ \gamma=1.4 \text{ Given} \end{pmatrix}

\frac{P_{2}}{P_{1}} = (2)^{1.4} = 2.64

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