Question

a)Estimate how long it takes for the cold air to fall out when you open the door of your refrigerator. For simplicity, assume your fridge is a cube of height 1 meter, and that the cold air inside is 5% denser than the warm air outside. Imagine that you remove the top and bottom of this cube and that the cold air just falls out as a solid block, without mixing with the warm air it moves through.
b)The ideal gas law P V = N k T, relates the pressure P and the (absolute!) temperature T of an idealized gas consisting of N particles in a box of volume V (here k is a constant which will not matter for us). If air was an ideal gas, and the density difference between the air inside and outside the refrigerator is 5% (but the pressure is the same), what is the temperature difference between inside and outside?

Answer 1

a) How far does it have to fall? Assume one meter.
Don't forget there is a buoyancy effect. Net downward force is
[1.05*density)*V - (density)*V]*g = M*a = (1.05)*density*a

"density" is ambient density

a = (0.05/1.05) g = 0.47 m/s^2

(1/2) a t^2 = 1 m when
t^2 = (1 m)*(4.25 s^2/m)
t = 2.1 s