Question

On heating a block its volume increases
by 0.30% for a rise of 100°C in its
temperature. Then coefficient of areal
expansion of that metal is
(A) 2 x 10 41°C
5
(B) 2 x 10-5/°C
(C) 2 x 10-6/°C
7
(D) 2 x 10-7/°C​

Answer 1

Given:

ΔV = 0.3 % of V = 0.003 V

ΔT = 100 °C

To Find:

The coefficient of areal  expansion of the given metal.

Calculation:

- The formula for the coefficient of volume expansion is:

γ = ΔV / VΔT

⇒ γ = 0.003 V / (V × 100)

⇒ γ = 0.00003 / °C

- The relation between the coefficient of areal expansion β and the coefficient of volume expansion γ is given as:

β = 2γ / 3

⇒  β = (2 × 0.00003) / 3

⇒  β = 0.00002 / °C = 2 x 10⁻⁵/ °C

- So, the correct answer is option (B) 2 x 10⁻⁵/°C

Answer 2

Given : on heating a block its volume increases by 0.30% for a rise of 100°C in its temperature.

To find : The coefficient of areal expansion of that metal.

solution : we know,

change in volume is given by, ∆v = vγ∆T

here ∆v = 0.30% of v

so, 0.30/100 × v = vγ × 100°C

⇒3 × 10¯³ = γ × 100

⇒γ = 3 × 10^-5 /°C

but we know, α/1 = β/2 = γ/3

⇒β = 2γ/3 = 2 × 3 × 10^-5/3 = 2 × 10^-5 /°C

Therefore the coefficient of areal expansion is 2 × 10^-5/°C .

therefore option (B) is correct choice.

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