How much work is done by a gas expanding at a constant temperature?

Question

A cylinder fitted with a piston contains 5.00L of a gas at a pressure of 4.00atm. The entire apparatus is contained in a water bath to maintain a contant temp. of 298K. The piston is released and the gas expands until the pressure inside the piston is 1atm. Assume ideal gas behavior and calculate the amount of work done by the gas as it expands at a constant pressure.

Answer 1

The gas is expanding at constant TEMPERATURE. Your starting conditions are 5 L and 4 atm. If your pressure decreases by a factor of 4, your volume increases by a factor of 4 (PV=constant isothermally) So your end condition is 20 liter and 1 atm. I believe work is the PV product as Int d(PV), where Int= a definite Integral. Since they are related as shown above, the Int term becomes Int d(PV)= Constant [Int dV/V+Int dP/P]
Work= 20*[ ln(V2/V1) + ln (P2/P1)]