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 the pressure in#"Pa"# , let's say. It doesn't matter in this case.#V# is the volume in#"L"# .#n# is the number of#\mathbf("mol")# s of gas#R# is the universal gas constant, which will be, based on our units,#"0.083145 L"cdot"bar/mol"cdot"K"# .#T# is the temperature in 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")#