Finding the Optimal Mass for a Pressure Cooker Cover

[derekjn]

Homework Statement

A pressure cooker is a sealed pot designed to cook food with the steam produced by boiling water somewhat above 100 C. Consider a pressure cooker with a weight of mass m covering the only hole (which has a diameter d = 0.003 m) on top of it. What should m be in order to cook food at 120 C. Assume the atmospheric pressure outside the cooker is 1 atm.

Homework Equations

Pressure = Force/Area
Saturated vapor pressure of water at 120 C = 1.99 x 10^5 Pa

The Attempt at a Solution

Since P = F/A, F = AP. F must then at least equal the weight mg of the weight at the top of the pressure cooker in order to lift it and let steam escape. So m = AP/g. The result I get from this approach is incorrect. Any help would be greatly appreciated.

 

[rl.bhat]

Will you please show your calculation?

 

[derekjn]

PA = mg

m = PA/g

where P is the pressure inside the cooker, A is the area of the hole, and m is the mass of the weight.

$$m = \frac{(1.99)(10^{5})(\pi)(0.003^{2})}{(9.8)} = 0.574 kg$$

 

[rl.bhat]

Have you taken into account the atmospheric pressure?

 

[derekjn]

Yes, I tried to include the difference in pressures (199,000 Pa - 101,300 Pa) as P in the equation, but still came up with an incorrect answer.

 

[rl.bhat]

Area = pi*d^2/4