# Homework Help: Spherical bubble rises to surface, Ideal Gas, Thermal Energy

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1. Dec 4, 2014

### MaryCate22

1. The problem statement, all variables and given/known data
A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 ∘C, and the radius of the bubble is 5.00 × 10^−3 m. At the surface, the pressure is 1.00 atm and the temperature of the water is 20.0 ∘C.

A) What is the final-to-initial volume ratio for the expanding bubble?

B) What is the change in thermal energy of the bubble?

2. Relevant equations
For part B: P1V1/T1=P2V2/T2

For part A: I honestly have no idea. I've tried messing around with change in thermal energy = N*Cv*deltaT
but I'm not getting any where.

3. The attempt at a solution
This problem is under the section for isobaric and isothermal ideal gas processes, but I'm not seeing how it is either.

2. Dec 4, 2014

### Bystander

Try swapping the hint for part B for part A.

3. Dec 5, 2014

### ehild

You can use this equation to answer question A. You know P1 and T1 deep in the water, and you know P2 and T2, at the surface. What is V2/V1?

4. Dec 5, 2014

### Staff: Mentor

To do part B, you are going to have to know the number of moles in the bubble. You can get this from the initial condition using the ideal gas law. What is it? After that you can get the final volume using the ideal gas law again , knowing the number of moles, the temperature and the pressure.

5. Dec 5, 2014

### MaryCate22

Sorry guys, I meant to put P1V1/T1=P2V2/T2 for Part A. I have that part. Part B is what is getting me, finding the change in thermal energy.

6. Dec 5, 2014

### ehild

Yo can find N from the ideal gas law : PV=NRT if N is the mol number. You know delta T. And air consist mostly of two-atomic molecules, with f=5 degrees of freedom.