Question

A thin brass sheet at 10 degrees celsius has the same surface area as a thin steel sheet at 20 degrees celsius. At what common temperature, if any, will the two sheets have the same area

Answer 1

They both will have same area at a temperature of -3.75°C

Explanation :

We know that co-efficient of linear expansion of brass = 19 x 10⁻⁶/°C

co-efficient of linear expansion of steel = 11 x 10⁻⁶/°C

let us assume they both settle at a temperature t with same area, if that exists

change in temp of brass = t - 10

change in temp of brass = t - 20

with area constant,

α₁t₁ = α₂t₂

=> α₁/α₂ = t₂/t₁

=> 19 x 10⁻⁶/11 x 10⁻⁶ = (t - 20)/(t - 10)

=> (t - 20)/(t - 10) = 19/11

=> 19t - 190 = 11t - 220

=> 19t - 11t = -220 + 190

=> 8t = -30

=> t = -3.75°C

Hence they both will have same area at a temperature of -3.75°C

Answer 2

hey...this is ur ans.

Title: Measurement of Thermal Radiation Properties of Solids. NASA SP-31

Authors: Richmond, J. C.

Journal: Measurement of Thermal Radiation Properties of Solids. NASA SP-31, 587 pages, published by NASA, Washington, D.C., 1963

Bibliographic Code: 1963NASSP..31.....R