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A thermally insulated piece of metal is heated under atmospheric pressure by an electric current so that it receives electric energy at a constant power P. This leads to an increase of absolute temperature T of the metal with time t as follows:
`T(t)=T_0[1+a(t-t_0)]^(1//4)`. Here, a, `t_0` and `T_0` are constants. The heat capacity `C_p(T)` of the metal is

A

`(4P)/(aT_(0))`

B

`(4PT^(3))/(aT_(0)^(4))`

C

`(2PT^(3))/(aT_(0)^(4))`

D

`(2P)/(aT_(0))`

Text Solution

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The correct Answer is:
B
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