Question

The gas inside of a container exerts `12 Pa` of pressure and is at a temperature of `120 ^o C`. If the temperature of the gas changes to `540 ^oK` with no change in the container's volume, what is the new pressure of the gas?

Answer 1

The new pressure is `16.5Pa`

Explanation:

We use the ideal gas law to calculate the change in pressure. The law is written:

`PV=nRT` where

`P` is the pressure of the gas,
`V` is the volume of the gas,
`n` is the number of moles of gas particles,
`R` is the universal gas constant and
`T` is the temperature in degrees Kelvin of the gas.

In our problem, only the temperature and pressure change - everything else is a constant. So let's gather all of the constant terms on one side of the equation as follows:

`P/T=(nR)/V = "constant"`

We can use this to calculate the unknown pressure:

`P_1/T_1=P_2/T_2`

Rearranging to find `P_2`

`P_2 = (P_1*T_2)/T_1=(12Pa*540 color(red) cancel( color(black)K))/((120+273)color(red) cancel( color(black)K))=16.5Pa`

Where we have added 273 to the temperature in Celsius to convert to Kelvin.