Answer:
a) Workdone = 0 Joules
b) Workdone = -286.48 Joules
Explanations:
The formula for work done in gas expansion is given as:
W = -P(V₂ - V₁)
where W is the workdone, P is the pressure, V₁ is the initial volume of the gas, and V₂ is the final volume of the gas.
Initial volume, V₁ = 264 mL = 264/1000 = 0.264L
Final volume, V₂ = 971 mL = 971/1000 = 0.971L
a) Workdone by the gas if it expands against a vacuum
When a gas expands against a vacuum, the external pressure, P = 0
Therefore, the workdone against a vacuum is:
W = 0(0.971 - 0.264)
W = 0 J
b) Workdone by the gas against a constant pressure of 4.00 atm
W = -P(V₂ - V₁)
W = -4(0.971 - 0.264)
W = -4(0.707)
W = -2.828 L atm
To convert workdone from L atm to Joules, multiply by 101.3
W = -2.828 x 101.3
W = -286.48 J
The workkdone has a negative sign because this is gas expansion, and work is done by the system