Question

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

Answer 1

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))`