The gas inside of a container exerts #6 Pa# of pressure and is at a temperature of #360 ^o K#. If the pressure in the container changes to #42 Pa# with no change in the container's volume, what is the new temperature of the gas?

1 Answer
Jun 14, 2017

Answer:

#3000# #"K"#

Explanation:

To solve this problem, we can use the pressure-temperature relationship of gases, illustrated by Charles's law:

#(P_1)/(T_1) = (P_2)/(T_2)#

Our known quantities are

  • #P_1 = 6# #"Pa"#

  • #T_1 = 360# #"K"#

  • #P_2 = 42# #"Pa"#

Since we're trying to find the final temperature, let's rearrange this equation to solve for #T_2#:

#T_2 = (P_2T_1)/(P_1)#

Plugging in the known quantities, we have

#T_2 = ((42cancel("Pa"))(360"K"))/(6cancel("Pa")) = color(red)(3000# #color(red)("K"#

rounded to #color(blue)(1# significant figure, the lowest amount given in the problem.