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

The resulting pressure is 300 kilopascals.

Step-by-step 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
`(V_(1))/(V_(2)) = 2` and
`P_(1) = 150\,kPa`, then the resulting pressure is:

`P_(2) = P_(1)* (V_(1))/(V_(2))`

`P_(2) = 300\,kPa`

The resulting pressure is 300 kilopascals.