1.

A horizontal tube, open at both ends, contains a column of liquid. The length of this liquid column does not change with temperature. Let γ = coefficient of volume expansion of the liquid and α = coefficient of linear expansion of the material of the tube. (a) γ = α(b) γ = 2α (c) γ = 3α (d) γ = 0

Answer»

Correct answer is: (b) γ = 2α 

Let A0 and At be the areas of cross-section of the tube at temperatures 0 and t respectively,

 I = length of the liquid column (constant)

V0 and Vt be the volumes of the liquid at temperatures 0 and t respectively,

V0 = lA0 Vt = lAt

Vt = V0(1 + γt) At = A0(1 + 2αt)

∴ Vt = lA0(1 + 2αt) = V0(1 + γt) = lA0(1 + γt)

or γ = 2α.



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