Question

A closed vessel of volume 80 litres contain gas at a gauge pressure of 150 kPa. If the gas is compressed isothermally to half its volume, determine the resulting pressure.

Answer 1

Answer:

The resulting pressure is 300 kilopascals.

Explanation:

Let consider that gas within the closed vessel behaves ideally. By the equation of state for ideal gases, we construct the following relationship for the isothermal relationship:

$P_{1}\cdot V_{1} = P_{2} \cdot V_{2}$ (1)

Where:

$P_{1}$, $P_{2}$ - Initial and final pressure, measured in kilopascals.

$V_{1}$, $V_{2}$ - Initial and final volume, measured in litres.

If we know that $\frac{V_{1}}{V_{2}} = 2$ and $P_{1} = 150\,kPa$, then the resulting pressure is:

$P_{2} = P_{1}\times \frac{V_{1}}{V_{2}}$

$P_{2} = 300\,kPa$

The resulting pressure is 300 kilopascals.