The coefficient of linear expansion `'alpha`' of the material of a rod of length `l_(0)` varies with absolute temperature as `alpha = aT -bT^(2)` where a & b are constant. The linear expansion of the rod when heated from `T_(1)` to `T_(2) = 2T_(1)` is :-

Options

A. (a)`((3)/(2)aT_(1)^(2) - (7b)/(3)T_(1)^(3))L_(0)`
B. (b)`(4a -(7b)/(3))T_(1)L_(0)`
C. (c)`(2aT_(1)^(2) - (7b)/(3)T_(1)^(3))L_(0)`
D. (d)None of these

Answer

A

Explanation

`because dl = alphal_(0)dT therefore Deltal = intdl = underset(T_(1))overset(T_(2))int(aT-bT^(2)) l_(0)dT`
= `l_(0)[(a)/(2)(T_(2)^(2) - T_(1)^(2)) - (b)/(3)(T_(2)^(3) - T_(1)^(3))] = [(3)/(2)aT_(1)^(2) - (7b)/(3)T_(1)^(3)] l_(0)`