Question

Three immiscible liquids are filled in a container as shown. The base area of the container is A and coefficient of cubical expansion of the material of the container is 3, while the coefficient of cubical expansion of the liquids are shown in the figure. The temperature of the system is increased byAT. If the answer for volume of the liquid flown AlyAT out of the container is then write the value of n in answer sheet. , п 2y 3 3y​

Answer 1

Explanation:

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Answer 2

The liquid flowing out of the container is (1/2)ALγΔT .

Explanation:

Given:

Coefficient of cubical expansion of the material of the container = 3/2 γ

Base area = A

Coefficient of cubical expansion of three immiscible  liquids are γ ,  2γ,  3γ

Height is L/3 each.

Temperature increased is ΔT

We have to find volume of the liquid flown off the container.

We know that, expansion of volume is

ΔV = V.γ . ΔT

ΔV = A.L.γ .ΔT

Where

A = base area

L = length of the liquid

γ =  volume coefficient expansion

ΔT = increase in temperature

Here, the total volume expansion due to three immiscible liquid,

Δ$V_{L}$ = Δ$V_{1}$ + Δ$V_{2}$ + Δ$V_{3}$

⇒ (AL/3).γ.ΔT +  (AL/3).2γ.ΔT + (AL/3).3γ.ΔT

⇒ 6ALγΔT/3

⇒ 2ALγΔT

Now, volume of expansion of the container,

Δ$V_{c}$ = V'.γ '.ΔT

⇒ A.L.3/2γ.ΔT

Here, L' = (L/3)3 = L

The difference of volume of liquid and container,

I.e. The liquid flowing out

Δ$V_{L}$ - Δ$V_{c}$  = 2ALγΔT - (3/2)ALγΔT

⇒ (1/2)ALγΔT

Final answer:

Hence the liquid flowing out of the container is (1/2)ALγΔT .

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