If an otherwise empty pressure cooker is filled with air of room temperature and
ID: 1463706 • Letter: I
Question
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 F120 on the lid when the air inside the cooker had been heated to 120C? Assume that the temperature of the air outside the pressure cooker is 20C (room temperature) and that the area of the pressure cooker lid is A. Take atmospheric pressure to be pa. Treat the air, both inside and outside the pressure cooker, as an ideal gas obeying pV=NkBT. Express the force in terms of given variables.
2)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 pa. 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 120C. What is the magnitude of the net force F20 on the lid when the air inside the cooker has cooled back down to 20C? Express the magnitude of the net force in terms of given variables.
Explanation / Answer
from the charles law :
With constant volume, P is proportional to T. So when T increases by 120C/20C or 393.15K/293.15K, P increases by the same factor.
So P2 = P1T2/T1 and net P = P2-P1;
thus net P = P1(T2/T1-1) = P1(T2-T1)/T1 = 101325*100/293.15 Pa.
F(120) = P*A
For the second phase, P = 101325 Pa again; the final net P will be P1(1-T1/T2) = P1(T2-T1)/T2 = 101325*100/393.15 Pa.
F(20) = P*A.
here F(120) is outward and F(20)is inward