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Statement-1: Temperature of a rod is inc...

Statement-`1`: Temperature of a rod is increased and again cooled to same initial temperature then itsfinal length is equal to original length provided there is no deformation take place.
Statement-`2`: For a small temperature change , length of a rod varies as `l = l_(0)(1+alphaDeltaT)` provided `alpha DeltaT ltlt1`. Here symbol have their usual meaning.

A

Statement -`1` is True , Statement -`2` is True , Statement -`2` is correct explanation for Statement - `1`

B

Statement -`1` is True , Statement -`2` is True , Statement -`2` is not correct explanation for Statement - `1`

C

Statement -`1` is True , Statement -`2` is False.

D

Statement -`1` is False , Statement -`2` is True.

Text Solution

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The correct Answer is:
B
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Statement I: The expanded length l of a rod of original length l_0 is not correctly given by (assuming alpha to be constant with T) l=l_0(1+alphaDeltaT) if alphaDeltaT is large. Statement II: It is given by l=l_0e^(alphaDeltaT) , which cannot be treated as being approximately equal to l=l_0(1+alphaDeltaT) for large value a DeltaT .

A cylindrical rod of length l, thermal conductivity k and area of cross section A has one end in a furnace maintained at constant temperature. The other end of the rod is exposed to surrounding. The curved surface of the rod is well insulated from the surrounding. The surrounding temperature is T_(0) and the furnace is maintained at T_(1) = T_(0) + DeltaT_(1) . The exposed end of the rod is found to be slightly warmer then the surrounding with its temperature maintained T_(2) = T_(0) + DeltaT_(2) [DeltaT_(2) ltlt T_(0)] . The exposed surface of the rod has emissivity e. Prove that DeltaT_(1) is proportional to DeltaT_(2) and find the proportionality constant.

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