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A current carrying wire heats a metal ro...

A current carrying wire heats a metal rod. The wire provides a constant power P to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod change with the (t) as `T(t)=T_(0)(1+betat^(1//4))` where `beta` is a constant with appropriate dimension of temperature. the heat capacity of metal is :

A

`(4P (T(t) - T_0 )^3)/(beta^4 T_0^4) `

B

`(4P(T(t) - T_0) )/(beta^4 T_0^2) `

C

`(4P (T(t) - T_0)^4)/(beta^4 T_0^5)`

D

`(4P (T (t) - T_0 )^4)/(beta^4 T_0^3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(4P (T(t) - T_0 )^3)/(beta^4 T_0^4) `
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