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
The answer is here.
https://en.wikipedia.org/wiki/Free_expansion
∆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.
To determine the sign of work (W) done when a gas expands into a vacuum, we can refer to the equation W = -PΔV, where W represents work, P is the pressure, and ΔV is the change in volume.
In this scenario, the gas is expanding into a vacuum, which means there is no pressure acting on the gas (P = 0). Substituting this value into the equation, we have W = -0ΔV, which simplifies to W = 0.
Therefore, the answer is option 5: ZERO. When a gas expands into a vacuum, no work is being done by the gas.