Specific Heat Capacity

JEE Advanced 2019 Paper 1, Question 3

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

(1) $\begin{equation*} T(t) = T_0 (1 + \beta t^{\frac{1}{4}}) \end{equation*}$

where $\beta$ is a constant with appropriate dimension while $T_0$ is a constant with dimension of temperature. The heat capacity of the metal is,

$\frac{4 P [T(t) - T_0]^3}{\beta^4 T_0^4}$
$\frac{4 P [T(t) - T_0]^4}{\beta^4 T_0^5}$
$\frac{4 P [T(t) - T_0]^2}{\beta^4 T_0^3}$
$\frac{4 P [T(t) - T_0]}{\beta^4 T_0^2}$

Solution

The heat capacity of an object is defined by the relation

(2) $\begin{equation*} \Delta Q = C \Delta T \end{equation*}$

where $\Delta Q$ is the heat that the object absorbs and $\Delta T$ is the resulting temperature change of …

Tag: Specific Heat Capacity

Rod heated by wire