Calculating Fridge Suction Force: Ideal Gas and Hermetic Door

[cathode-ray]

Homework Statement

Consider a fridge with a volume of 120L whose door has 0.8m of height and 0.5m of length. When the door is open there isn't a relevant change in the air quantity inside the fridge. However the temperature increases slightly.
Suppose that when the door is opened, the air inside the fridge reaches an uniform temperature of -8 ºC, and is in equilibrium with the outside atmosferic pressure. When the door is closed, the air inside the fridge cools down until it reaches a temperature of -10 ºC. The air inside the fridge is considered an ideal gas and the door of the fridge is completely hermetic.

Homework Equations

Calculate the force needed to reopen the door.

The Attempt at a Solution

I don't know how to approach this problem

 

[tiny-tim]

hi cathode-ray!

hint: pressure

 

[cathode-ray]

Hi tiny-tim!

I tried to think using your hint. However the result i get is still different from the one given in the solution, despite they are very close. I thought this way:

When the door is open the pressure applied to the air inside the fridge is the atmospheric pressure P=1.013E5 Pa. The volume is 120E-3 m^3, and the temperature is -8+273.15=265.15 K. Using the ideal gas law i get the number of moles of the air inside the fridge.

When the door is closed there are two forces with opposite directions applied to it: the pressure of the air inside the fridge and the atmospheric pressure. So the force needed to open the door is the difference between these two pressures times the area of the door. I again used the ideal gas law to calculate the pressure caused by the inner air, using the number of moles i got (n=5.514) and the temperature of -10+273.15=263.15K.

The finally result was F=320 N, but the solution is 306 N.

What am I doing wrong?

 

[tiny-tim]

When the door is closed there are two forces with opposite directions applied to it: the pressure of the air inside the fridge and the atmospheric pressure. So the force needed to open the door is the difference between these two pressures times the area of the door.

Your method looks correct (except you haven't taken account of the fact that the fridge door opens on a hinge) …

there must be a numerical error somewhere

 

[cathode-ray]

Sorry for the time I took to answer.

I found out why it is different from the result of the solutions. The problem are the approximations. I tried different approximations and i got the result of the solutions.

Thanks for your help