Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 86

Initially a household freezer compartment is filled with air at room temperature \(T_i = 27.0^\circ\text{C}\). Then the door is closed and the cooling in the walls is turned on until the air temperature is at the recommended value of \(T_f = -18.0^\circ\text{C}\). The door has height \(h = 0.600\text{ m}\) and width \(w = 0.760\text{ m}\), with hinges on the left edge (and thus with a rotation axis there) and a handle on the right edge. Assume that the freezer is airtight. What are (a) the pressure difference \(\Delta p\) between the inside and outside of the door, (b) the net force \(F\) on the door from that pressure difference, and (c) the force \(F_a\) needed to open the door by pulling on the handle perpendicular to the door?