Express the density of a solid substance varying with temperature

[endeavor]

I need to show that the density of a solid substance varies with temperature as d = d₀(1 - 3aT), where a is the thermal coefficient and T is the change in temperature.

I know V = V₀ (1 + 3aT) and V = m/d. Since m is constant,

d₀ = d(1 + 3aT)
d₀ - d₀3aT = d + d3aT - d₀3aT
d₀(1 - 3aT) = d +3aT(d - d₀)

Am I now supposed to assume that the d only changes a little compared to d₀, so that (d - d₀) = 0?

 

[mukundpa]

do = d(1 + 3aT)
d = do/(1+3aT) = do(1+3aT)^-1

now expanding using binomial theorem and as a is very small the higher terms can be neglected, gives

d = do(1- 3aT + ...)


MP