Expansion of a basketball with temperature

[BittersweetLove]

Another problem with an equation I don't know.I'm sooo going to fail this test if I don't get some help...


A basketball with a volume of 4.75 Liters is left in a car when the temperature is 298 K. What will the volume of the ball be as the car heats up to 309 K during the day?

 

[berkeman]

That's not a very well-stated question. The answer depends whether the ball can expand or is rigid. And if it can expand, it depends on whether the car windows are open, etc.

Assume it can't expand, then the volume is the same, right? Assume it can expand per the Ideal Gas Law -- write out that equation and solve it for us to check your work.

 

[BittersweetLove]

I'm a bit confused because isn't the Ideal Gas Law equation

Pressure (x) Volume = # of moles (x) 0.0821 atm (x) Temperature?

If I do that equation, I have the volume and temperature, but what about the pressure and moles? I don't even know how I would find mol in the problem.

 

[berkeman]

The number of moles inside the closed basketball is constant. The pressure, however, goes to my objection about the problem statement. If the ball is rigid, the pressure increases and the volume does not. If the ball is flacid, the volume changes and the pressure does not. In the real world, the ball's walls have an elastic constant, and the expansion of the ball does work against this spring action.

So the simplistic answer would be to hold P and n constant, anc calculate the change in V from the change in T (remember to use absolute temp). But that is so simplistic, that there must be more to the problem statement, it would seem...

 

[BittersweetLove]

There's no more to it. Promise. Maybe if there were, I wouldn't be so confused. lol.