Question

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 changes with time (t) as T (t) = Tₒ (1 + βt¹៸⁴ )
where β is a constant with appropriate dimension while Tₒ is a constant with dimension of temperature.
The heat capacity of the metal is

A. 4P(T(t)-Tₒ)⁴ B. 4P(T(t)-Tₒ)
β⁴Tₒ⁵ β⁴Tₒ²


C. 4P(T(t)-Tₒ)² D. 4P(T(t)-Tₒ)³
β⁴Tₒ² β⁴Tₒ⁴

Answer 1

Explanation:

ANSWER

dQ=HdT

dtdQ=H⋅dtdT

P=H.T0.β.41.t−3/4

T0⋅β4P=t−3/4.H

Now, T−T0=T0βt1/4

So t3/4=(T0βT−T0)3

∴H=T04β44P(T−T0)3

correct option 2.