First slide

Thermal expansion

Question

Radius of a sphere is 100cm at 0°C and 100.1cm at 100°C. Coefficient of cubical expansion of the sphere is

Easy

A

30 × 10^–6/C
B

10 × 10^–6/°C
C

60 × 10^–6/°C
D

20 × 10^–6/°C

Solution

Given that R₁= 100cm, R₂ = 100.1cm; t₁ = 0⁰C; t₂ = 100⁰C $α = \frac{100.1 - 100}{100 (100)} = 10 \times 10^{- 6} / 0_{C}$
We have,

$\large \alpha =\frac {R_2-R_1}{R_1(\Delta t)}=\frac {101.1-100}{100(100)}=10\times 10^{-6}/^0C$

then
$\large \gamma =3\alpha=3(10\times 10^{-6})=30\times 10^{-6}/^0C$

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