A current carrying wire heats a metal rod

PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

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

) is the metal rod changes with time (

t

) as

T(t) = T_0(1 + \beta t^{2/4})

. Where

\beta

is a constant with appropriate dimensions while

T_0

is a constant with dimensions of temperature. The heat capacity of metal is : (1)

\frac{4P(T(t) - T_0)}{\beta^4 T_0^2}

(2)

\frac{4P(T(t) - T_0)^2}{\beta^4 T_0^3}

(3)

\frac{4P(T(t) - T_0)^4}{\beta^4 T_0^5}

(4)

\frac{4P(T(t) - T_0)^3}{\beta^4 T_0^4}