Question

The gas inside of a container exerts `5 Pa` of pressure and is at a temperature of `190 ^o K`. If the pressure in the container changes to `32 Pa` with no change in the container's volume, what is the new temperature of the gas?

Answer 1

New temperature of the gas is `1216^oK`

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 `5Pa` of pressure and is at a temperature of `190^oK`. When pressure of the gas changes to `32Pa`, if the temperature becomes `T_2`, we should have

`5/190=32/T_2` or `T_2=((190xx32)/5)`

i.e. `P_2=6080/5=1216^oK`.