Final answer:
To calculate the work done by a gas during isobaric expansion, use the formula W = PΔV, convert pressure and volume to SI units, and multiply by the conversion factor. For an expansion of a gas from 2.0 L to 29.8 L at a constant pressure of 3.14 atm, the work done is approximately 8798.9 J.
Step-by-step explanation:
To calculate the work done by a gas during an isobaric expansion, we can use the formula W = PΔV, where W is work, P is pressure, and ΔV is the change in volume. Since we're dealing with pressure in atmospheres (atm) and volume in liters (L), it's important to convert these values to consistent SI units for work calculation (joules, J). 1 L·atm is equivalent to 101.3 J.
First, we need to calculate the change in volume, which is ΔV = final volume - initial volume = 29.8 L - 2.0 L = 27.8 L. The pressure is given as 3.14 atm. To convert the work into joules, we use the conversion factor:
W = PΔV * 101.3 J/L·atm
Substituting our values, we get:
W = 3.14 atm * 27.8 L * 101.3 J/L·atm
= 8798.892 J
Therefore, the work done by the gas on its surroundings is approximately 8798.9 J.