Question

If you seal a container of air at room temperature (20.0 degrees celcius) and then put it in the refrigerator (2.00 degrees celcius) what will the pressure inside the container be? Assume atmospheric pressure equal to 100,000 Pa.

Answer 1

The pressure inside the container will be 9.39×10⁴Pa

At constant volume, the pressure in a container is directly proportional to its absolute temperature.

If air in a container is sealed at 20⁰C at a pressure equal to the atmospheric pressure and cooled to 2.00⁰C, the pressure inside the container falls.

Convert the temperature in Celsius to Kelvin.

$T_1=20.0^oC+273.15=293.15K\\T_2=2.00^oC+273.15=275.15K$

Use the expression for the pressure law.

$\frac{P_2}{P_1} =\frac{T_2}{T_1}$

Substitute 100,000 Pa for P₁, 293.16 K for T₁ and 275.15K for T₂.

$\frac{P_2}{P_1} =\frac{T_2}{T_1}\\ P_2=P_1(\frac{T_2}{T_1})\\ =(100,000Pa)(\frac{275.15K}{293.15K} )\\ =9.386*10^4Pa$

The pressure in the container (correct to 2 sf) is 9.39×10⁴Pa