# The gas inside of a container exerts 12 Pa of pressure and is at a temperature of 30 ^o K. If the temperature of the gas changes to 200 ^oK with no change in the container's volume, what is the new pressure of the gas?

Mar 5, 2016

The new pressure of the gas will be $80 P a$.

#### Explanation:

Pressure $P$, volume $V$ and temperature $T$ (in Kelvin) have the relation $P \frac{V}{T} = k$ where $k$ is a constant.

As there is no change in the container's volume, it means that ${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$

In the given case, gas inside of a container exerts $12 P a$ of pressure and is at a temperature of ${30}^{o} K$. When the temperature of the gas changes to ${200}^{o} K$, if the pressure becomes ${P}_{2}$, we should have

$\frac{12}{30} = {P}_{2} / 200$ or ${P}_{2} = \left(\frac{200 \times 12}{30}\right)$

i.e. ${P}_{2} = \frac{2400}{30} = 80$ $P a$.