Question

A metal is heated from 0°C to 500°C and its density reduces to of its original density
The coefficient of linear expansion for this metal, considering it constant for the given range of
temperature is (a = 10-5/°C)​

Answer 1

question -> A metal is heated from 0°C to 500°C and its density reduces to 1/1.027 of its original density. Determine the coefficient of linear expansion for this metal, considering it constant for the given range of temperature.

solution : let coefficient of linear expansion of this metal is α.

let mass of the metal is m and volume is v

so density of metal , d = m/v

when temperature increases,

density of the metal object, d' = m/v'

= m/v(1 + 3α∆T).......(1)

a/c to question,

density reduces to 1/1.027 of its original density.

so, d' = d/1.027 = m/1.027v .....(2)

from equations (1) and (2) we get,

v(1 + 3α∆T) = 1.027v

⇒1 + 3α(500°C - 0°C) = 1.027

⇒3α × 500 = 0.027

⇒α = 0.027/1500 = 1.8 × 10¯⁵/°C

Therefore the coefficient of linear expansion of the metal is 1.8 × 10¯⁵/°C