Question

An iron rod is subjected to cycles of magnetisation at the rate of 50Hz. Given the density of the rod is $8 \times {10^3}kg/{m^3}$and specific heat is $0.11 \times {10^{ - 3}}cal/kg{}^ \circ C$. The rise in temperature per minute, if the area enclosed by the B – H loop corresponds to energy of ${10^{ - 2}}J$ is
A. $78{}^ \circ C$
B. $88{}^ \circ C$
C. $8.1{}^ \circ C$
D. None of these

Answer 1

Hint: Magnetization of an object is defined as the process through which a substance is made a temporary or permanent magnet by exposing them to an external magnetic field. In order to find the solution of the given question enlist all the given physical quantities and apply the formula of thermodynamics to find the required solution.
Formula Used: $Q = mc\Delta T$

Complete answer:
It is given in the question,
Rate of magnetisation is defined as the process through which a substance is made a permanent or temporary magnet by exposing them to an external magnetic field with time.
Rate of magnetisation = 50Hz
Density of the rod = $8 \times {10^3}kg/{m^3}$
Specific heat = $0.11 \times {10^{ - 3}}cal/kg{}^ \circ C$
Energy of the B – H loop = ${10^{ - 2}}J$$ = {10^{ - 2}} \times 60$
First law of thermodynamics explains that heat is a form of energy and all thermodynamic processes are subject to the principle of conservation of energy, which means that the heat energy can neither be created nor be destroyed. It can only be transferred from one position to another and can be converted to and from other forms of energy.
$Q = mc\Delta T$
This equation gives us the amount of heat supplied ‘Q’, to a material of mass ‘m’ and specific heat capacity ‘c’.
$ \Rightarrow \Delta T = \dfrac{{50 \times 60 \times {{10}^{ - 2}}}}{{8 \times {{10}^3} \times 0.11 \times {{10}^{ - 3}} \times 4.2}} = 8.10{}^ \circ C$
Thus, the rise in temperature per minute will be $8.10{}^ \circ C$.

Hence, option (C) is the correct option.

Note:
The Magnetic behaviour of a magnet is characterized by the alignment of the atoms inside a substance. When a ferromagnetic substance is brought under the application of a strong external magnetic field, they experience a torque where the substance aligns themselves in the direction of the magnetic field applied and hence gets strongly magnetized within the direction of the magnetic field. Induced magnetisation is defined as the process through which a non-magnetic material is magnetized by bringing it under the influence of an external magnetic field.