Calculating Force on Pressure Cooker Lid with Changing Temperature

In summary, a pressure cooker is a pot that can be tightly sealed to prevent gas from entering or escaping. When an empty pressure cooker is filled with air and heated on a stove, the net force on the lid can be calculated using the Guy-Lussac law, which states that p/T is constant. In the first part, the force on the lid is found to be 0.34Ap_a. In the second part, where the pressure relief valve is opened and the air cools back down to room temperature, the net force is found to be Ap_a - (293.15Ap_a)/(393.15). This is because the resultant force is inwards, with the magnitude being the outer force minus the inner force.
  • #1
CurtisB
16
0

Homework Statement


A pressure cooker is a pot whose lid can be tightly sealed to prevent gas from entering or escaping.


1-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 C Assume that the temperature of the air outside the pressure cooker is 20degrees C (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 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 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 C.

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 C?
Express the magnitude of the net force in terms of given variables.

Homework Equations


delta_U = n*C_v*delta_T
pV = N*k_B*T
F=pA

The Attempt at a Solution


I am really stuck with this one, at first I tried re-arranging the equation given in terms of V to equate final and initial but that didn't work, can someone please give me a push in the right direction.
Cheers.
 
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  • #2
CurtisB said:

Homework Statement


A pressure cooker is a pot whose lid can be tightly sealed to prevent gas from entering or escaping.


1-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 C Assume that the temperature of the air outside the pressure cooker is 20degrees C (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 variables.


Since V,N and k_B (R) is unaltered by this process of heating the air up inside of the pot we have that

[tex]\frac{p}{T} = constant[/tex]

which is known as the Guy-Lussac law.
 
  • #3
Thanks, that really helped, I got the answer to part one to be 0.34Ap_a but now the second part is getting me. I work out the final pressure inside to be
(293.15p_a)/(393.15) so the force out = (293.15Ap_a)/(393.15), then the force in equals -Ap_a so the final answer should be (293.15Ap_a)/(393.15)-Ap_a, right, but apparently I have the signs mixed up, am I right in saying that net force acting out is the out force minus the in force?
 
  • #4
Well the answer was actually F = Ap_a - (293.15Ap_a)/(393.15), can anyone tell me why the two forces are swapped around, int the first part it was the inside force minus the outside force so why is this the outside force minus the inside force, wouldn't the second part be a negative value because the force is now pushing in from the outside, ie , the direction of the force has changed.
 
  • #5
CurtisB said:
Thanks, that really helped, I got the answer to part one to be 0.34Ap_a ...

How did you get to this answer?
 
  • #6
if [tex]pV=Nk_BT[/tex] then [tex]\frac{p}{T} = \frac{Nk_B}{V} = constant[/tex] so [tex]\frac{p_f}{T_f}=\frac{p_i}{T_i}[/tex], convert [tex]^oC[/tex] to K so [tex]\frac{p_f}{393.15}=\frac{p_i}{293.15}[/tex] and because [tex]p=\frac{F}{A}[/tex] and [tex]p_i = p_a[/tex], [tex]\frac{F}{A}=\frac{393.15p_a}{293.15}[/tex] so [tex]F=\frac{393.15AP_a}{293.15}=1.34Ap_a[/tex] and since the force on the outside acting in = [tex]Ap_a[/tex] then[tex]1.34Ap_a - Ap_a = 0.34Ap_a[/tex]
 
Last edited:
  • #7
Ok, now I am on the same page as you.

CurtisB said:
Well the answer was actually F = Ap_a - (293.15Ap_a)/(393.15), can anyone tell me why the two forces are swapped around, int the first part it was the inside force minus the outside force so why is this the outside force minus the inside force, wouldn't the second part be a negative value because the force is now pushing in from the outside, ie , the direction of the force has changed.


The problem just wants the resultant force on the top, not taking the direction of the force into consideration. The inner pressure is now lower than the outer pressure. So the resultant force will be inwards and its magnitude is the outer force minus the inner force.
 
  • #8
CurtisB said:
and since the force on the outside acting in = [tex]Ap_a[/tex] then

How do we know that the force outside acting in is A*P_a?
Isn't it just A since p(outside)= 1atm ?
 
Last edited:

What is the formula for calculating force on a pressure cooker lid?

The formula for calculating force on a pressure cooker lid is F = P x A where F is force, P is pressure, and A is the area of the lid.

How does temperature affect the force on a pressure cooker lid?

As temperature increases, the pressure inside the pressure cooker also increases. This leads to an increase in force on the lid.

Can the force on a pressure cooker lid be too high?

Yes, if the force on the lid exceeds the strength of the lid or the material it is made of, it can lead to the lid breaking or exploding.

How can I accurately measure the force on a pressure cooker lid?

The force on a pressure cooker lid can be measured using a pressure gauge or by using a calibrated weight placed on top of the lid and measuring the resulting pressure.

What safety precautions should I take when using a pressure cooker?

When using a pressure cooker, it is important to follow the manufacturer's instructions and safety precautions. This may include making sure the lid is properly sealed, not overfilling the cooker, and releasing pressure before opening the lid. It is also important to use caution when handling hot liquids and steam from the pressure cooker.

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