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A thermally insulated piece of metal is ...

A thermally insulated piece of metal is heated under atmosphere by an electric current so that it receives electric energy at a constant power P. This leads to an increase of the absoulute temperature T of the metal with time t as follows `T=a^(1/4)`. then the heat capacity `C_(p)` is

A

`(4PT^(3))/(a^(4))`

B

`4PT^(2))/a^(3)`

C

`4PT^(2)`

D

None of these

Text Solution

Verified by Experts

a) `therefore dH=Pdt` `therefore C_(p) = (Pdt)/(dT) = (P/(dT)/(dt))`
Here, `T=at^(1/4)` or `T/a = t^(1/4)` `therefore t=(T^(4)/a^(4))`
`therefore (dT)/(dt) = a/4(T/a)^(-3) = a/4(T/a)^(-3) = (a^(4))/(4T^(3)) rArr C_(p) = (P)/(dT)/(dt)` = `(4PT^(3))/(a^(4))`
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