First slide

Thermal expansion

Question

The coefficient of volume expansion of glycerine is $49 \times 10^{- 5 \circ} C^{- 1}$ . What is the fractional change in density for a 30^o C rise in temperature?

Moderate

A

0.0155
B

0.0145
C

0.0255
D

0.0355

Solution

Given, $γ = 49 \times 10^{- 5 \circ} C^{- 1},$
$∆ T = 30^{\circ} C$
$V' = V + ∆ V = V (1 + γ ∆ T)$
$∴$ $V' = V (1 + 49 \times 10^{- 5} \times 30) = 1.0147 V$
$∵$ $ρ = \frac{m}{V} and ρ^{'} = \frac{m}{V^{'}} = \frac{m}{1.0147 V} = 0.9855 ρ$
Hence, fractional change in density
$= \frac{ρ - ρ^{'}}{ρ} = \frac{ρ - 0.9855 ρ}{ρ} = 0.0145$

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