calculate the work performed if a balloon contracts from 12.32L to 422 ml due to an extermal pressure of 3.1 atm
To calculate the work performed when a balloon contracts, we need to use the equation for work in thermodynamics. The equation is:
Work = -P * ΔV
Where:
- Work is the work performed on the system (balloon) in Joules (J)
- P is the external pressure in atmospheres (atm)
- ΔV is the change in volume of the system in liters (L)
Given:
- External pressure (P) = 3.1 atm
- Initial volume (V1) = 12.32 L
- Final volume (V2) = 422 mL
First, we need to convert the final volume from milliliters to liters:
V2 = 422 mL = 0.422 L
Next, we can calculate the change in volume:
ΔV = V2 - V1 = 0.422 L - 12.32 L = -11.898 L
Since the balloon is contracting, the change in volume (ΔV) will be negative.
Now, we can substitute the values into the equation for work:
Work = -P * ΔV = -(3.1 atm) * (-11.898 L)
Calculating the work:
Work = (3.1 atm) * (11.898 L)
Work = 36.858 J
Therefore, the work performed on the system (balloon) is approximately 36.858 Joules.