Final answer:
The work done by the gas is calculated as the product of the external pressure and the change in volume, resulting in a value of -506625 J, where the negative sign indicates work done by the gas.
Step-by-step explanation:
The work done by a gas during expansion or compression can be calculated by the product of the external pressure and the change in volume. Given that the external pressure is 1.0 atm (which is equivalent to 101325 Pa), and the piston is pushed out by 500 cm (which is 5 meters since 100 cm = 1 meter), the cross-sectional area of the container is 1 m².
To calculate work (W), we use the formula:
W = -PΔV
Since pressure (P) is constant at 1.0 atm (101325 Pa), and the change in volume (ΔV) is the product of the cross-sectional area (A) and the displacement of the piston (d), we get:
ΔV = A * d = 1 m² * 5 m = 5 m³
W = -101325 Pa * 5 m³ = -506625 J
The negative sign indicates that work is being done by the gas on the surroundings. To express this work in joules, which is the SI unit for work or energy, we include the conversion from liters-atmospheres to joules:
W = -506625 J (since 1 L·atm = 101.32 J and we have already used the conversion from atm to Pa).