The gas inside of a container exerts #12 Pa# of pressure and is at a temperature of #360 ^o 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
Aug 18, 2017

Answer:

#T_2 = 1920# #"K"#

Explanation:

We're asked to find the final temperature of a gas, given some pressure and temperature information.

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 and quantity of gas)

where

  • #P_1# and #P_2# are the initial and final pressures of the gas

  • #T_1# and #T_2# are the initial and final absolute temperatures of the gas (which must be in Kelvin)

We know:

  • #P_1 = 12# #"Pa"#

  • #P_2 = 64# #"Pa"#

  • #T_1 = 360# #"K"#

  • #T_2 = ?#

Plugging these in:

#(12color(white)(l)"Pa")/(360color(white)(l)"K") = (64color(white)(l)"Pa")/(T_2)#

#color(red)(ulbar(|stackrel(" ")(" "T_2 = 1920color(white)(l)"K"" ")|)#