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Question

By what temperature a rod should be heated so that it's length becomes 2l0 if initial length is l0 . Assume that α (coefficient of linear expansion) in that range of temperature remains constant and melting point is very high.

A
2α
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B
1α
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C
ln2α
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D
ln1α
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Solution

The correct option is C ln2α
α=1LdLdtbtwl=l(1+αΔT)
Original form
Note:Here expansion is too large to use this approximation.
2l0l0dLL=T2T1αdTlnL|2l0l0=α(TαT1)ln(2l0)lnl0=αΔTαΔT=ln2ΔT=ln2α
A very large number btw

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