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?

1 Answer
Mar 7, 2016

Answer:

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.