Final answer:
The work done by a gas during expansion is calculated with the formula w = -PextΔV, and in an isothermal, quasi-static expansion to four times its original volume is given by pV(ln 4). A positive work value indicates that energy is transferred out from the gas.
Step-by-step explanation:
The work done by a gas during an expansion can be computed using the formula w = -PextΔV, where ΔV is the change in volume (Vfinal - Vinitial), and Pext is the external pressure. In an isothermal, quasi-static expansion, where a gas expands to four times its original volume, the work done by the gas is given by pV(ln 4), with p and V being the initial pressure and volume respectively. Since work is equal to the negative of the pressure times the change in volume, during an expansion, work is positive meaning that energy is transferred out from the gas.
It's important to note that when calculating work done by the gas during an expansion, we often deal with volume in liters and pressure in atmospheres, but the unit of work is usually expressed in joules. The conversion factor of 1 L'atm to 101.32 J allows us to convert our final answer into the more commonly used joule unit.