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A cubical block is floating inside a bath . The temperature of system is increased by small temperature ∆T. It was found that the depth of submerged portion of cube does not change. Find the relation between coefficient of linear expansion (alpha) of the cube and volume expansion of liquid (Y).?
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A cubical block is floating inside a bath . The temperature of system ...
Introduction:
When a cubical block is floating inside a bath and the temperature of the system is increased by small temperature ∆T, the depth of the submerged portion of the cube does not change. In this scenario, we need to find the relation between the coefficient of linear expansion (alpha) of the cube and volume expansion of liquid (Y).

Explanation:
When the temperature of the system is increased by ∆T, the volume of the cube and the liquid both increase. However, the depth of the submerged portion of the cube remains unchanged. This means that the increase in the volume of the cube is compensated by the increase in the volume of the displaced liquid.

Formula:
The volume of the displaced liquid is equal to the volume of the submerged portion of the cube. Let V be the volume of the cube, A be the surface area of the cube, L be the length of the side of the cube, Y be the volume expansion of the liquid, and alpha be the coefficient of linear expansion of the cube. Then we can write:

V = AL
∆V = V(alpha)∆T
∆V = YA∆T
∆V = V(alpha)∆T = YA∆T
(alpha) = Y/L

Conclusion:
Hence, we can conclude that the coefficient of linear expansion (alpha) of the cube is equal to the volume expansion of liquid (Y) divided by the length of the side of the cube (L).
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A cubical block is floating inside a bath . The temperature of system ...
Y=3ALFA
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A cubical block is floating inside a bath . The temperature of system is increased by small temperature ∆T. It was found that the depth of submerged portion of cube does not change. Find the relation between coefficient of linear expansion (alpha) of the cube and volume expansion of liquid (Y).?
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