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Two rods of lengths l(1) and l(2) are ma...

Two rods of lengths `l_(1) and l_(2)` are made of materials having coefficients of linear expansion `alpha_(1) and alpha_(2)` respectively. What could be the relation between above values, if the difference in the lengths of the two rods does not depends on temperature variation?

Text Solution

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The difference in length is `l=l_(1)-l_(2)` (assuming that `l_(1)gtl_(2)`)
As l is independent of temperature
`(Deltal)/(DeltaT)=0`
`implies(Deltal_(1))/(DeltaT)-(Deltal_(2))/(DeltaT)=0`
As we know that `Deltal=lalphaDeltaT`
`implies(Deltal)/(DeltaT)=lalpha`
So, we get
`l_(1)alpha_(1)-l_(2)alpha_(2)=0` or `l_(1)alpha_(1)=l_(2)alpha_(2)`
this is the desired result.
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