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Question

A liquid which has coefficient of volumetric expansion of γ, is heated till there is a temperature change of ΔT. The density of the liquid after heating is.
(initial density ρ)

A
ρ=ρ(1+γΔT)
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B
ρ=ρ γΔT
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C
ρ=ρ(1γΔT)
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D
ρ=ρ+γΔT
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Solution

The correct option is C ρ=ρ(1γΔT)
We know that
m=ρV=ConstantρVf=ρiViρV=ρ{V(1+γ×ΔT)}ρ=ρ1+γΔTρ=ρ(1γΔT)
Becasue γΔT<<1

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