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Express the density of a solid substance varying with temperature 
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#1
Feb2306, 11:19 PM

P: 176

I need to show that the density of a solid substance varies with temperature as d = d_{0}(1  3aT), where a is the thermal coefficient and T is the change in temperature.
I know V = V_{0} (1 + 3aT) and V = m/d. Since m is constant, d_{0} = d(1 + 3aT) d_{0}  d_{0}3aT = d + d3aT  d_{0}3aT d_{0}(1  3aT) = d +3aT(d  d_{0}) Am I now supposed to assume that the d only changes a little compared to d_{0}, so that (d  d_{0}) = 0? 


#2
Feb2406, 07:21 AM

HW Helper
P: 505

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 


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