Problem: A gas is compressed by an adiabatic process that decreases its volume by a factor of 2.In this process, the pressureA. increases by a factor of more than 2.B. increases by a factor of 2.C. does not change.D. increases by a factor of less than 2.

FREE Expert Solution

When a gas is compressed by an adiabatic process, we have the condition:

$\overline{){\mathbf{P}}{{\mathbf{V}}}^{{\mathbf{\gamma }}}{\mathbf{=}}{\mathbf{c}}{\mathbf{o}}{\mathbf{n}}{\mathbf{s}}{\mathbf{t}}{\mathbf{a}}{\mathbf{n}}{\mathbf{t}}}$

This implies that:

$\begin{array}{rcl}{{\mathbf{P}}}_{{\mathbf{1}}}{{{\mathbf{V}}}_{{\mathbf{1}}}}^{{\mathbf{\gamma }}}& \mathbf{=}& {{\mathbf{P}}}_{{\mathbf{2}}}{{{\mathbf{V}}}_{{\mathbf{2}}}}^{{\mathbf{\gamma }}}\\ {{\mathbf{P}}}_{{\mathbf{2}}}& \mathbf{=}& \frac{{{\mathbf{P}}}_{{\mathbf{1}}}{{{\mathbf{V}}}_{{\mathbf{1}}}}^{{\mathbf{\gamma }}}}{{{{\mathbf{V}}}_{{\mathbf{2}}}}^{{\mathbf{\gamma }}}}\end{array}$

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Problem Details

A gas is compressed by an adiabatic process that decreases its volume by a factor of 2.

In this process, the pressure

A. increases by a factor of more than 2.

B. increases by a factor of 2.

C. does not change.

D. increases by a factor of less than 2.