if an otherwise empty pressure cooker is filled with air of room temperature and

Question

if an otherwise empty pressure cooker is filled with air of room temperature and then placed on a hot stove, what would be the magnitude of the net force F on the lid when the air inside the cooker had been heated to 120C? Assume that the temperature of the air outside the pressure cooker is 20C (room temperature) and that the lid of the pressure cooker has a diameter of 20 cm. Take atmospheric pressure to be 1 bar. Treat the air, both inside and outside the pressure cooker, as an ideal gas. Remember that there is pressure on both sides of the lid, so the net force on the lid is a combination of the downward force due to the pressure of the outside air and the upward force due to the pressure of the inside air.

Explanation / Answer

Force (F) = Pressure (P) * Area (A)

Area = 3.142 * r * r

Net Force: F(120C) = [P(120C) - P(20C)]* A -----------(1)

As per ideal gas law:

PV = nRT---------- (2)

Since the volume V and # moles n do not change at 120 and 20 C, we have,

P(120)/T(120) = P(20)/T(20)

therefore, P(120) = P(20)*T(120)/T(20) -------- (3)

Substituting this in eq 1

Net Force = [p(20)*T(120)/T(20) - P(20)]* A

=[1 * 120/20 -1]*3.142 * (0.2/2)^2 = 0.157 N

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