# What is the temperature of a 100 liter container having 1 mole of an ideal gas at a pressure of 20 kilopascals?

Jan 19, 2017

This can only occur at a temperature of 240.5 kelvin (-32.6 °C).

#### Explanation:

For an ideal gas, the relationship among pressure, volume, quantity and temperature is the ideal gas law

$P V = n R T$

This essentially tells us that if we specify any three of $P , V , n \mathmr{and} T$ the fourth is no longer variable, but rather is fixed by the choice of the first three.

Using the values stated in this problem,

$\left(20\right) \left(100\right) = \left(1\right) \left(8.315\right) T$ where $R = 8.315$ is the gas constant for the units stated. Therefore

$T = \frac{\left(20\right) \left(100\right)}{\left(1\right) \left(8.315\right)} = 240.5 K$

The only temperature for which the stated conditions could exist would be at a temperature of 240.5 kelvin (-32.6 °C).