Question

Given that W = -PatmΔV, if a gas expands into a vacuum, the sign of W is ?

1. Positive: work is being done on the gas
2. Negative: work is being done on the gas
3. Positive: work is being done by the gas
4. Negative: work is being done by the gas
5. ZERO: no work is being done by the gas

Answer 1

The answer is here.
https://en.wikipedia.org/wiki/Free_expansion

Answer 2

∆U = ∆H + P∆V
If P∆V is negative => ∆U = ∆H + (- P∆V) => ∆U = ∆H - P∆V
For work = - P∆V the particles of an expanding gas will lose energy => exothermic and will perform work on the surroundings.
You can generalize this … expansion work for system < O => work is exothermic
When a gas is compressed, particles gain energy and work is endothermic.