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
Truong-Son N.
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 #1# represented an initial state and state #2# a final state, we have #P_1 -> P_2# and #T_1 -> T_2#, but #V_1 = V_2 = V# and #n_1 = n_2 = n#.

With this information we get two ideal gas law relationships:

#P_1V = nRT_1#
#P_2V = nRT_2#

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 #T_2# for an ideal gas.

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

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

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