Question

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?

Answer 1

The new pressure of the gas will be `80 Pa`.

Explanation:

Pressure `P`, volume `V` and temperature `T` (in Kelvin) have the relation `PV/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 `12Pa` of pressure and is at a temperature of `30^oK`. When the temperature of the gas changes to `200^oK`, if the pressure becomes `P_2`, we should have

`12/30=P_2/200` or `P_2=((200xx12)/30)`

i.e. `P_2=2400/30=80` `Pa`.