Question

The length of an edge of a cube increases by 2% when it is heated by 50 degree Celsius. The percentage increase in volume will be;

a. 8
b. 4%
c. 2%
d. 6
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Answer 1

Given info : The length of an edge of a cube increases by 2% when it is heated by 50°C.

To find : The percentage increase in volume will be...

solution : first find coefficient of linear expansion.

let edge length of a cube is a.

using formula, ∆l = l₀α∆T

if it is heated by 50°C , edge length increases by 2%.

so, 2% of a = a × α × 50

⇒α = 2/(100 × 50) = 4 × 10¯⁴/°C

so coefficient of volume expansion, γ = 3α = 4 × 10¯⁴/°C = 1.2 × 10¯³/°C

now ∆V = V₀ × γ × ∆T

⇒∆V/V₀ = 1.2 × 10¯³/°C × 50°C

⇒∆V/V₀ × 100 = percentage change in volume = 60 × 10¯³ × 100 = 6 %

Therefore percentage change in volume is 6 %

Shortcut :

percentage change in volume = 3 × percentage change in edge length, if percentage change in edge length is less than 10% .