Finding the Optimal Mass for a Pressure Cooker Cover

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AI Thread Summary
To determine the optimal mass for a pressure cooker cover to achieve cooking at 120 C, the pressure inside the cooker must be calculated using the saturated vapor pressure of water at that temperature, which is 1.99 x 10^5 Pa. The force exerted by the mass must equal the pressure multiplied by the area of the hole, calculated as A = π(d^2)/4, where d is the hole's diameter of 0.003 m. The equation m = PA/g is used to find the mass, where P is the internal pressure and g is the acceleration due to gravity. Attempts to factor in atmospheric pressure have led to confusion, as the correct pressure difference should be used in calculations. The final calculated mass needed is approximately 0.574 kg.
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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.
 
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Will you please show your calculation?
 
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
 
Have you taken into account the atmospheric pressure?
 
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.
 
Area = pi*d^2/4
 
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