Question

In a quasi-static isobaric expansion, 500 J of work is done by the gas. If the gas pressure is 0.80 atm, what is the fractional increase in the volume of the gas, assuming it was originally at 20.0 L?

(a) 0.04
(b) 0.02
(c) 0.10
(d) 0.08

Answer 1

The fractional increase in the volume of the gas during a quasi-static isobaric expansion where the gas does 500 J of work at 0.80 atm is approximately 0.10, which is answer option (c).

Step-by-step explanation:

To solve for the fractional increase in the volume of the gas during the quasi-static isobaric expansion, we must first understand that in such an expansion, the work done (W) by the gas is equal to the pressure (P) multiplied by the change in volume (ΔV). Since work is done by the gas, it is considered as positive work. The formula relating them is W = P * ΔV. We also need to convert pressure from atm to joules per liter using the conversion factor 1 atm = 101.3 J/L.

The pressure given is 0.80 atm, which we convert to J/L: P = 0.80 atm * 101.3 J/L/atm = 81.04 J/L. We know the work done by the gas is 500 J. Using the formula for work, we rearrange to find ΔV: ΔV = W / P = 500 J / 81.04 J/L = 6.17 L. The original volume of the gas is 20.0 L, so the fractional increase in volume is ΔV / V_initial = 6.17 L / 20.0 L = 0.3085. The closest option to this actual increase is 0.10 or (c).