Rod heated by wire

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,

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


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 …

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