[Rimi]

The air inside a refrigerator (volume 100 L) is cooled from 20 °C to 0 °C after closing the door.
What is the force needed to open the refrigerator door (area 1 m²)? The refrigerator is supposed
to be air-tight.

I really have no clue how to approach this problem. When the temperature decreases the volume also decreases..ok. I know Force = Pressure x Area, but I don't think that will help at all.

[Borek]

Volume is constant, so it is the pressure that goes down.

[jaspevacek]

Use the ideal gas law to calculate the pressure after cooling, and then use the formula you provided.

[Rimi]

That's what I figured, but what is the initial pressure? That's what I'm not understanding. Unless my answer is supposed to be in terms of pressure?

[Borek]

Start with 1 atm.

[fledarmus]

If you've opened the door to put something in, the pressure inside the refrigerator is the same as the pressure outside the refrigerator - 1 atm. Cooling doesn't start (in your example) until the door is closed, so the initial pressure when you begin cooling is also 1 atm.

[Rimi]

Thanks I got it.

[billnotgatez]

would you like to share your results

[Rimi]

would you like to share your results

Wouldn't that be against the rules if someone came by with the same question?

[billnotgatez]

Wouldn't that be against the rules if someone came by with the same question?
 

I will have to ask Socrates - philosophy was not my strong suit.
 

I am assuming your class is done with this question and has been graded on for you and your classmates.

by the way
We often check peoples results to let them know if they did it right so long as they show all work.

You can send me a private message to help my curiosity if you want
 

[fledarmus]

would you like to share your results

Wouldn't that be against the rules if someone came by with the same question?

Oh no, you are allowed to answer your own questions - and it makes us feel good to know that you got the right answer 

[billnotgatez]

Since this has been posted for a while and the homework has probably been graded, I thought I would attempt to solve this as a exercise in honing my skills.

With the variables
P as pressure
V as volume
n as amount of substance (moles)
T as temperature
R as the universal gas constant
using the ideal gas law formula
PV=nRT
rearrange
PV/nT=R
for before refrigerator is closed
P₁V₁/n₁T₁=R
for after refrigerator is closed and cooled
P₂V₂/n₂T₂=R
since R is a constant
P₁V₁/n₁T₁=
   P₂V₂/n₂T₂
since the volume before and after are the same
since the moles before and after are the same
P₁/T₁=P₂/T₂
multiplying both sides by T₂
P₂=P₁T₂/T₁
Given
Force = Pressure x Area
Door area = 1 m²
V₁ = V₂ = 100 L
T₁ = 293.15K (20C) T₂ = 273.15K (0C)
assumed
P₁ = 1 atm (Atmosphere)
looked up
1 atm = 101325 pascal (Pa)
Then
P₂= ((101325Pa)(273.15K))/(293.15K)
P₂= 94412.156745693331059184717721303
rounding
P₂= 94412 Pa
Thus
outside the refrigerator is P₁ = 101325 Pa
inside  the refrigerator is P₂ =  94412 Pa
The difference between inside and outside pressure = 6913 Pa
recollect the given
area of the refrigerator door is 1 m2
force = pressure x area
looked up
1 Pa = 1 N/m²  where N is newton and m is meter
Since the door is 1m² the force to open = 6913 N

[Wastrel]

I was really surprised by the answer, which for me was in kilograms, completely forgetting that they are not an 'acceptable' unit of force.

I did remember that doors have hinges.

[fledarmus]

Force = Pressure x Area, 

Can you calculate the pressure difference between the inside and the outside of the refrigerator? That would be the pressure you would have to overcome to open the door, and the force required would be related to that pressure and the area of the door.

[billnotgatez]

@fledarmus

I wrote

outside the refrigerator is P₁ = 101325 Pa
inside  the refrigerator is P₂ =  94412 Pa
The difference between inside and outside pressure = 6913 Pa

later

1 Pa = 1 N/m²  where N is newton and m is meter
Since the door is 1m² the force to open = 6913 N

Alternatively I could have said

outside the refrigerator is P₁ = 101325 Pa
inside  the refrigerator is P₂ =  94412 Pa
and
1 Pa = 1 N/m²  where N is newton and m is meter
Since the door is 1m²
the force outside the refrigerator is 101325 N
the force inside  the refrigerator is 94412 N
The difference between these forces is 6913 N
which is the force necessary to open the door

-----------

@fledarmus

Is the second way a better way of presenting the results,since the final answer in both is the same?
Or
is my physics rusty

@Wastrel

For me it would have been useful to couch what the force would be like by stating in lifting of grams against gravity. I do not have a since in my mind about newtons.

Example
The newtons are for opening the door feel the same as lifting a gram weight against gravity.

do you want to fill in the grams?