Final answer:
The work done by a system when a piston expands from a volume of 13.27 l to 76.55 l against a constant pressure of 14.89 atm is -95279.22 joules (J), indicating that work is done by the system on its surroundings.
Step-by-step explanation:
To calculate the work done by a system when a piston expands against a constant external pressure, the formula W = -PΔV can be used. Here, W represents work, P represents pressure, and ΔV is the change in volume. Since pressure is given in atmospheres (atm) and volume in liters (L), the work will initially be calculated in liter-atmospheres (L·atm).
First, we need to determine the change in volume of the system ΔV, which is the final volume minus the initial volume. So, ΔV = 76.55 L - 13.27 L = 63.28 L. Given the pressure P is 14.89 atm, the work done is W = -14.89 atm × 63.28 L = -940.3992 L·atm. We then convert this to joules using the conversion factor 1 L·atm = 101.32 J. Hence, the work done in joules is W = -940.3992 L·atm × 101.32 J/L·atm = -95279.22 J.
The negative sign indicates that work is done by the system on its surroundings as the system expands.