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Consider a rod of length 'l'. When heated, its temperature got increased by 't'.

Increase in its length = l[itex]\alpha[/itex]t.

total length be (l1) = l + l[itex]\alpha[/itex]t.

Again the rod is heated and the temperature further got increased by 't'.

Total length be l2.

l2 can be calculated in two ways,

l2 = l1 + l1[itex]\alpha[/itex] t......(a)

0r l2 = l + l[itex]\alpha[/itex](2t)........(b)

Equating (a) and (b).

l1 + l1[itex]\alpha[/itex] t = l+l[itex]\alpha[/itex](2t)

{l + l[itex]\alpha[/itex]t} + {l + l[itex]\alpha[/itex]t}{[itex]\alpha[/itex] t}

= l+l[itex]\alpha[/itex](2t).

Solving above equation we get l([itex]\alpha[/itex]t)

Where am i going wrong?

Increase in its length = l[itex]\alpha[/itex]t.

total length be (l1) = l + l[itex]\alpha[/itex]t.

Again the rod is heated and the temperature further got increased by 't'.

Total length be l2.

l2 can be calculated in two ways,

l2 = l1 + l1[itex]\alpha[/itex] t......(a)

0r l2 = l + l[itex]\alpha[/itex](2t)........(b)

Equating (a) and (b).

l1 + l1[itex]\alpha[/itex] t = l+l[itex]\alpha[/itex](2t)

{l + l[itex]\alpha[/itex]t} + {l + l[itex]\alpha[/itex]t}{[itex]\alpha[/itex] t}

= l+l[itex]\alpha[/itex](2t).

Solving above equation we get l([itex]\alpha[/itex]t)

^{2}= 0.Where am i going wrong?

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