The gas inside of a container exerts #"24 Pa"# of pressure and is at a temperature of #"75 K"#. If the temperature of the gas changes to #"125 K"# with no change in the container's volume, what is the new pressure of the gas?

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Answer 1 · 2018-05-22T18:39:01

#40Pa#

the pressure law states that 'the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.'
[source: http://chemistry.bd.psu.edu/jircitano/gases.html]

direct proportion is a form of direct variation, meaning that #P# and #T# increase at the same rate.

in direct proportion, they are linked by a constant. since #P prop T#, #P# is a constant multiplied by T.

in shorter notation, #P = kT#.

to find the constant here, use the two values of pressure and Kelvin temperature given: #24Pa# and #75K#.

if P = kT, then k = P / T.

#P / T = 24 / 75 =8 / 25 = 0.32#

#k = 0.32#

using the same constant, we know that for this fixed volume (since the temperature changes with no change in volume),

#P = 0.32T#.

here, #T# is #125K#.

#P# (in #Pa#) #= 0.32 * 125#

#= 40#

the new pressure #P# is #40Pa#.