# The gas inside of a container exerts #"84 Pa"# of pressure and is at a temperature of #"320 K"#. If the pressure in the container changes to #"64 Pa"# with no change in the container's volume, what is the new temperature of the gas?

##### 1 Answer

Apr 1, 2016

One way to do this is to use the ideal gas law and derive an equation.

#PV = nRT# where:

#P# is thepressurein#"Pa"# , let's say. It doesn't matter in this case.#V# is thevolumein#"L"# .#n# is thenumber of#\mathbf("mol")# sof gas#R# is theuniversal gas constant, which will be, based on our units,#"0.083145 L"cdot"bar/mol"cdot"K"# .#T# is thetemperaturein units of#"K"# .

Then, we would say that if state

With this information we get two ideal gas law relationships:

Therefore, to find the new temperature, we can divide these to get:

#P_1/P_2 = T_1/T_2#

#\mathbf(T_2 = T_1*P_2/P_1)#

So, now that we have the final equation, we can acquire

#color(blue)(T_2) = "320 K" xx (84/64)#

#=# #color(blue)("420 K")#