Answer:
a) V1 = 4V - V2/3 and V2 = 4V - 3V1
b) Δe = 4000V - 4000V2 + 9000V1
Explanation:
Let V be the volume of the box with two compartments
V1 is for the left compartment
V2 is for the right compartment
Momentum for the compartments before impact:
3000V1 + 1000V2
Momentum after the impact:
V(3000 + 1000) = 4000V
a) To find the volume of each compartment, V1 and V2, we note:
Momentum prior to impact = Momentum post-impact
3000V1 + 1000V2 = 4000V
Thus, V1 = (4000V - 1000V2)/3000 = 4V - V2/3
And V2 = (4000V - 3000V1)/1000 = 4V - 3V1
b) The change in entropy, Δe = 4000V1 - 1000V2
Substituting for V1 and V2 gives:
4000(4V - V2)/3 - 1000(4V - 3V1)
Results in 16000V - 4000V2/3 - 4000V + 3000V1
Finally yielding Δe = 4000V - 4000V2 + 9000V1