Answer:
a) V1 = 4V - V2/3 and V2 = 4V - 3V1
b) Δe = 4000V - 4000V2 + 9000V1
Explanation:
Let V represent volume of the box containing the two compartments
V1 represents compartment of the left compartment
V2 represents compartment of the right compartment
Momentum of the compartments before impact:
3000V1 + 1000V2
Momentum of the compartments after impact:
V(3000 + 1000) = 4000V
a) To obtain the volume of each compartment, that is, V1 and V2, we say:
Momentum before impact = Momentum after impact
3000V1 + 1000V2 = 4000V
∴ V1 = 4000V - 1000V2/3000 = 4V - V2/3
Also, V2 = 4000V - 3000V1/1000 = 4V - 3V1
b) Change in entropy,Δe = 4000V1 - 1000V2
By substituting the V1 and V2, we have:
4000(4V - V2)/3 - 1000(4V - 3V1)
16000V - 4000V2/3 - 4000V + 3000V1
16000V - 4000V2 - 12000V + 9000V1
∴ Δe = 4000V - 4000V2 + 9000V1
A) The volume of each compartment in terms of V :
[tex]V_{1} = 4V - \frac{V_{2} }{3}[/tex]
[tex]V_{2} = 4V - 3V_{1}[/tex]
B) The change in the system's entropy during the process :
Δe = 4000V - 4000V₂ + 9000V₁
Given data:
V = ∑ V₁ + V₂ where ; V₂ = Volume of the right compartment, V₁ = volume of the left compartment
V₁ = 3000 particles
V₂ = 1000 particles
A) Determine Volume of each compartment when new equilibrium state is reached
Given that ; momentum before impact = momentum after impact
i.e. 3000V₁ + 1000V₂ = 4000V
∴ V₁ = [tex]4V - \frac{V_{2} }{3}[/tex] , V₂ = 4V - 3V₁
B) Determine the change in the system's entropy ( Δe )
Δe = 4000 V₁ - 1000 V₂
Insert the values of V₁ and V₂ into equation
∴ Δe = 4000V - 4000V₂ + 9000V₁
Hence we can conclude that The volume of each compartment in terms of V are as written above
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