What is the temperature of the freezer based on the Ideal Gas Law?

[Bgerst103]

Homework Statement

Here is the problem: You are worried that your -80C freezer is on the fritz. Unfortunately you do not have a thermometer. You do have a balloon. so, you blow up the balloon and measure that it has a diameter of 10cm when at 25C. you put it in the freezer, let it come to thermal equilibrium, and measure the new volume to be 9cm. What is the temperature of the freezer? (assume the balloon is a perfect sphere).

A) -55C
B) -66C
C) -77C
D) -88C

Homework Equations

I'm really not sure how do solve this with the given information. I am also unsure if the "new volume" is a typo and is actually supposed to be new diameter since the cm are not cubed.

The Attempt at a Solution

I've tried putting numbers in the equation P1V1/T1=P2V2/T2 but never been able to come out with any of those answers.

 

[Chestermiller]

Homework Statement

Here is the problem: You are worried that your -80C freezer is on the fritz. Unfortunately you do not have a thermometer. You do have a balloon. so, you blow up the balloon and measure that it has a diameter of 10cm when at 25C. you put it in the freezer, let it come to thermal equilibrium, and measure the new volume to be 9cm. What is the temperature of the freezer? (assume the balloon is a perfect sphere).

A) -55C
B) -66C
C) -77C
D) -88C

Homework Equations

I'm really not sure how do solve this with the given information. I am also unsure if the "new volume" is a typo and is actually supposed to be new diameter since the cm are not cubed.

The Attempt at a Solution

I've tried putting numbers in the equation P1V1/T1=P2V2/T2 but never been able to come out with any of those answers.

Did you remember to use absolute temperature? As far as the diameter issue is concerned, try it both ways and see if you match any of the answers.

Chet

 

[Bgerst103]

Did you remember to use absolute temperature? As far as the diameter issue is concerned, try it both ways and see if you match any of the answers.

Chet

What about the pressure calculation? It seems like there are too many variables missing to solve P1V1/T1=P2V2/T2. Is there a way to calculate the pressure of the balloon before it is in the freezer? I know the equation PV=nRT but n is unknown as well. Also, even if P1 can be calculated that still leaves two variables left. We did examples in lecture where only one variable was missing which is why this problem is more confusing. Am I missing some conceptual understanding of the problem where pressure isn't need or can be canceled out?

 

[Chestermiller]

What about the pressure calculation? It seems like there are too many variables missing to solve P1V1/T1=P2V2/T2. Is there a way to calculate the pressure of the balloon before it is in the freezer? I know the equation PV=nRT but n is unknown as well. Also, even if P1 can be calculated that still leaves two variables left. We did examples in lecture where only one variable was missing which is why this problem is more confusing. Am I missing some conceptual understanding of the problem where pressure isn't need or can be canceled out?

The pressure is assumed to stay constant at 1 atm.

Chet

 

[FermiAged]

What are the assumptions behind the ideal gas approximation? Does it matter whether the gas is air, N2, CO2 , He etc.?

 

[Chestermiller]

What are the assumptions behind the ideal gas approximation?

The pressure is low enough.

Does it matter whether the gas is air, N2, CO2 , He etc.?

No. Only the range of applicability.

Chet

 

[Bgerst103]

Did you remember to use absolute temperature? As far as the diameter issue is concerned, try it both ways and see if you match any of the answers.

Chet

Using 9 as the diameter I was able to get -55 C as an answer. Does that sound right to you? Thank you for your help.

 

[Chestermiller]

Using 9 as the diameter I was able to get -55 C as an answer. Does that sound right to you? Thank you for your help.

I get -56 C, but who's counting.

Chet