The gas inside of a container exerts #27 Pa# of pressure and is at a temperature of #150 ^o K#. If the pressure in the container changes to #30 Pa# with no change in the container's volume, what is the new temperature of the gas?

1 Answer
Jul 28, 2017

Answer:

#T_2 = 170# #"K"#

Explanation:

We'r asked to find the new temperature of a gas,after it is subjected to a pressure change with no change in volume.

To do this, we can use the pressure-temperature relationship of gases, illustrated by Gay-Lussac's law:

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

Here,

  • #P_1 = 27# #"Pa"#

  • #T_1 = 150# #"K"#

  • #P_2 = 30# #"Pa"#

  • #T_2 = ?#

Plugging in known values and solving for #T_2#, we have

#T_2 = (P_2T_1)/(P_1) = ((30cancel("Pa"))(150color(white)(l)"K"))/(27cancel("Pa")) = color(red)(170# #color(red)("K"#

rounded to #2# significant figures.