A perfectly fitting pot and its lid often stick after cooking

I encountered a question that asks for the reason that a perfectly fitting pot and its lid often stick after cooking when it cools down. The answer in the solution manual was that the pressure decreases when the temperature decreases. I understand that point, but my problem is the following: The pot before being heated during cooking is influenced only by the atmospheric value, and the food inside that pot is the atmospheric pressure also. So this is the initial state for the pressure inside the pot now. When heated the pressure inside the pot increases. When we let the pot cool down to the room tempreture, would the pressure return to its initial value which is the atmospheric pressure? Why does the solution manual consider a vacuum inside the pot?

• To see it in reverse, take a mason jar with one of those rubber seals, put room temperature water in it, close the jar, and place it in the fridge. Leave it for at least 30 minutes, and then take it out and try to open it - the rubber seal will be very snug to the jar! – N. Steinle Nov 11 '18 at 17:02

As @Stephen C. Steel pointed out, the pressure increase in the pot (due to heating the air in the pot) relative to the outside pressure exerts a net force on the lid causing it to vent. However, it doesn’t matter if the lid is on before the cooking process starts, or put on just before turning off the heat. The important thing is to understand the mechanism involved for the lid sticking on cool down.

Let’s assume the cooking starts with the lid off. Generally you will have some steam (water vapor) developed in the pot. The lid is put on just before turning off the heat. Inside the pot we have a mixture of air and water vapor, likely near saturation, which is nearly equal to the outside pressure, 1 atm. But the pressure inside the pot is the sum of the partial pressures of the water vapor and dry air. As the mixture cools the water vapors condenses into a liquid. The pressure in the pot is now less due to the loss of the partial pressure of the water vapor. The lower pressure in the pot versus the pressure outside the pot causes a force holding down the lid, if it consists of a relatively good seal.

I should add the fact that in addition to the drop in pressure due to condensation, the drop in temperature of the dry air in essentially a fixed volume also results in a pressure drop. Considering air as an ideal gas, from the ideal gas law:

$$\frac {P_1V_1}{T_!}=\frac {P_2V_2}{T_2}$$

And for $$V=$$constant

$$\frac {P_1}{T_!}=\frac {P_2}{T_2}$$

Since $$T_2, then $$P_2

Hope this helps

• Thanks for your answer . But there is a point here is the force difference between the outside and the inside pressure leads to the act of sticking where is the normal force that the pot produces on the lid If there is a Free body diagram on the lid of the pot it will have the forces from the pressure and the force provided from the pot on the lid why this normal force do not cancel the force result from the difference in pressures – A.ELAK Nov 11 '18 at 20:18
• RE: "However, it doesn’t matter if the lid is on before the cooking process starts, or put on just before turning off the heat." // That isn't true. The assumption is that the lid acts as a one way valve. It lets excess pressure out, but does not leak air in. Thus if the pot starts with the lid on, then some gas would escape as vapor pressure of water increases. This would sweep out some air. So if the pot had been boiling for some time all the air would be displaced and only water vapor would remain in the head space. – MaxW Nov 11 '18 at 20:46
• @MaxW Sure it can act as a one way valve. All I'm saying is you don't have to start with the lid on to get the sticking effect.. – Bob D Nov 11 '18 at 21:32
• @A.ELAK The weight of the lid is the minimum force necessary to remove the lid, whether or not your cooking with the pot. The cooling effect after cooking only adds to the force necessary to remove the lid due to the pressure drop inside. I don't see how the weight of the lid cancels out the effect of the pressure drop. Maybe I'm not understanding your comment. – Bob D Nov 11 '18 at 21:43
• In a sense, if you have a super mega heavy lid, and it is so heavy that air cannot escape and the lid becomes a perfect seal, then yes, it will "Cancel out". However, that's not how real lids work. If you tried this, the pot might just explode on you. A heavier lid may end up with less pressure difference because it is better at preventing air from escaping, but it is a heavier lid to begin with, and a boiling pot can create a huge amount of pressure. Not sure if you really gain any benefit in the end. If you're curious look up "exploding pressure cookers". – Nelson Nov 12 '18 at 6:23

You've made the wrong assumption about what a perfectly fitting lid does. Rather than sealing perfectly, it will vent gas when the interior is at a higher pressure (the lid will lift), but seal when the exterior pressure is higher (the lid is pressed down).