Blowing up a balloon (thermodynamics and maybe ideal gases)

[doctordiddy]

Homework Statement

A balloon behaves such that the pressure is P = CV3
where C
= 100 kPa/m3
. The balloon is blown up with air from a starting volume of 1 m3
to a volume
of 3 m3
. Find the work done by the air.

Homework Equations

W=PdV

The Attempt at a Solution

What I tried is simply trying the above solution by multiplying the P which is given by P=CV^3 by the change in volume

so i got

W=(CV^3)(Vf-Vi)

I then realized I had no idea what would the V in this equation be, can someone tell me if I am even doing this question right and if I am how I can determine the V?

Thanks

 

[KataKoniK]

for posting your attempt at a solution. It's great that you are trying to solve this problem on your own. However, there are a few things that need to be addressed in your solution attempt.

Firstly, the equation W = PdV is not relevant to this problem. This equation is used to calculate the work done in a reversible process, where the pressure is constant. In this problem, the pressure is not constant, so this equation cannot be used.

Secondly, the equation P = CV^3 is not the correct equation to use to describe the behavior of a balloon. This equation is not a physical law, and it does not accurately describe the behavior of a balloon. In fact, this equation does not have any physical meaning at all.

To solve this problem, you need to use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. In this problem, the temperature is constant, so the equation can be simplified to P = constant/V. This means that as the volume increases, the pressure decreases.

To find the work done by the air, you need to integrate the equation W = PdV from the initial volume (Vi = 1 m^3) to the final volume (Vf = 3 m^3). This will give you the total work done by the air in expanding the balloon. I hope this helps clarify the problem and guide you towards the correct solution. Good luck!