Question

Thermodynamic Processes: An ideal gas is compressed isothermally to one-third of its initial volume. The resulting pressure will be

Answer 1

The resulting pressure is 3 times the initial pressure.

Step-by-step explanation:

The equation of state for ideal gases is described below:

`P\cdot V = n \cdot R_(u)\cdot T` (1)

Where:

`P` - Pressure.

`V` - Volume.

`n` - Molar quantity, in moles.

`R_(u)` - Ideal gas constant.

`T` - Temperature.

Given that ideal gas is compressed isothermally, this is, temperature remains constant, pressure is increased and volume is decreased, then we can simplify (1) into the following relationship:

`P_(1)\cdot V_(1) = P_(2)\cdot V_(2)` (2)

If we know that
`(V_(2))/(V_(1)) = (1)/(3)`, then the resulting pressure of the system is:

`P_(2) = P_(1)\cdot \left((V_(1))/(V_(2)) \right)`

`P_(2) = 3\cdot P_(1)`

The resulting pressure is 3 times the initial pressure.