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Q.

The density of a liquid of coefficient of cubical expansion $γ$ is $ρ$ at 0^oC when the liquid is heated to a temp T, the change is density will be

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a

$\frac{ργT}{1 + γT}$

b

$\frac{- (1 + γT)}{γT}$

c

$\frac{- ργT}{1 + γT}$

d

$\frac{γ (1 + γT)}{γT}$

answer is A.

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Detailed Solution

$ρ_{1} = ρ, ρ_{2} = ρ_{2}; ∆ t = T$
change in density $ρ_{2} - ρ_{1} = \frac{ρ_{1}}{1 + γ ∆ t} - ρ_{1}$
$= ρ_{1} [\frac{1}{1 + γ ∆ t} - 1] = ρ_{1} [\frac{1 - 1 - γ ∆ t}{1 + γ ∆ t}] = ρ [\frac{- γT}{1 + γT}] = \frac{- γTρ}{1 + γT}$

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