Question

1)When the temperature of a metal wire is increased from 00C to 100C, its length increases by 0.02%. The percentage change in its mass density will be closest to

Answer 1

Change in the length of the metal wire (Δl) when its temperature is changed by ΔT is given by

 

Δl = lαΔT

Here, α = coefficient of linear expansion

 

Δl = 0.02%, ΔT = 100C

Therefore, α = Δl/lΔT

= 0.02/ (100 x 10)

⇒ α = 2 x 10-5

 

Volume coefficient of expansion, γ = 3α = 6 x 10-⁵

Since ρ = M/V

(ΔV/V) x 100 = γΔT = (6 x 10-5 x 10 x 100) = 6 x 10-²

 

Volume increase by 0.06% therefore density decreases by 0.06%

 

 

The density decreases by 0.06%.