First slide

Thermal expansion

Question

A rectangular block is heated from 0°C to 100°C. The percentage increase in its length is 0.10%. What will be the percentage increase in its volume ?

Moderate

A

0.03 %
B

0.10 %
C

0.30 %
D

none of these

Solution

Given $Δl / l = 0 \cdot 10 % = 0 \cdot 001 and ΔT = 100^{\circ} C$
Now $\frac{Δl}{l} = αΔT$
or $0 \cdot 001 = α \times 100 or α = 10^{- 5} /^{\circ} C$
Further $γ = 3 α = 3 \times 10^{- 5} /^{\circ} C$
$∴ \frac{ΔV}{V} = γΔT = (3 \times 10^{- 5}) (100) = 3 \times 10^{- 3}$
or $\frac{ΔV}{V} \times 100 = (3 \times 10^{- 3}) (100) = 0 \cdot 30 %$

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