Pressure cooker thermodynamics question...?

Question

So lets assume the pressure cooker uses a weight over a small opening in the lid. As the cooker heats up internal pressure increases until the weight is lifted slightly and the gas can escape.

If you know the mass of the weight, diameter of the lid and ambient air pressure...is it possible to figure out at what pressure gases will begin to escape from the cooker? (i.e., the weight gets lifted so gas can escape).

Answer 1

Yes, you can. This is pretty easy actually.

You know mass of the weight, so you know the force acting down which is just mass multiplied by the acceleration of gravity.

Now, to translate pressure into force, we have to realize that pressure is simply force / area. Thus, to find the force acting on the weight simply subtract atmospheric pressure from the internal pressure and multiply by the size of the opening.

let p_e = pressure at which gas escapes, p_0 = atm.
w = weight of mass (mass * gravity)
A = hole area

A(p_e - p_0) = w = m * g

solve for p_e



p_e = (w/A) + p_0

Thath's your answer.

Answer 2

You have to make some assumptions. Assume, say that the pressure of the gas is only acting on a circular area of the weight to lift it, and no upward force is being applied anywhere else. To find the pressure in the cooker divide the mass of the weight x g (9.81 x weight) by the area you've assumed.

There are a number of other assumtions here too. Firstly that the contents of the cooker is in equilibrium, and therefore that it is being supplied with energy in the form of heat at the same rate it is being lost as heat and kinetic energy (of the mving gas exiting the cooker.

The further question emerges of how much escaping gas the cooker loses, and how well the seals seal, to stop the gas being replenished. How little pressure is it possible to create in a pressure cooker?

Answer 3

Hi. The psi inside must be equal to the weight times the area of the small hole in square inches.

Answer 4

It is possible. F=Pressure * Area