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(A) A pressure cooker is a pot whose lid can be tightly sealed to prevent gas from entering or escaping. 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_120 on the lid when the air inside the cooker had been heated to 120 degrees Celsius? Assume that the temperature of the air outside the pressure cooker is 20 degrees Celsius (room temperature) and that the area of the pressure cooker lid is A. Take atmospheric pressure to be p_a. Treat the air, both inside and outside the pressure cooker, as an ideal gas obeying pV=N*k_B*T. Express the force in terms of given quantities.
(B) The pressure relief valve on the lid is now opened, allowing hot air to escape until the pressure inside the cooker becomes equal to the outside pressure p_a. The pot is then sealed again and removed from the stove. Assume that when the cooker is removed from the stove, the air inside it is still at 120 degrees Celsius. What is the magnitude of the net force F_20 on the lid when the air inside the cooker has cooled back down to 20 degrees Celsius? Express the magnitude of the net force in terms of given quantities.
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This solution uses the formula P1/T1 = P2/T2 because the volume is constant. All calculations are included for (a) and (b).
A) Let us assume the volume of pressure cooker be V,
Initial temperature T1= 20+273 = 293 k
Final temperature T2 = 120+273 = 393 k
Initial pressure P1 = 1 atm = p_a
Final pressure P2 = ...
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