Question

A resistance coil of $60\Omega$ is immersed in 42 kg of water. A temperature of 7A is passed through it. The rise in temperature of water per minute is
1. ${{4}^{\circ }}C$
2. ${{8}^{\circ }}C$
3. ${{1}^{\circ }}C$
4. ${{12}^{\circ }}C$

Answer 1

To solve this problem we will be using joule’s heating effect for heat developed or dissipates across the coil and total heat supplied to the system through convection and by equating both the equations we can calculate change in temperature of water.

Formula used:
Heat dissipates, $\Rightarrow H={{I}^{2}}Rt$
Heat supplied to the system, $\Rightarrow Q=mc\Delta T$

Complete Step by step solution:
Heat transfer is a process in which exchange of heat occurs from high temperature body to low temperature body when these systems are brought in contact with one another, which is given by
$\Rightarrow Q=mc\Delta T$, here Q (Heat supplied to the system), m (mass of the system), $\Delta T$(Change in temperature),
Given,$R=60\Omega$, $m=42kg$, $I=7A$ and time $t=1\min =60\sec$and total heat dissipates will be given as,
$\Rightarrow H={{I}^{2}}Rt$
Now by equating Q and H from above equations we have:
$\Rightarrow {{I}^{2}}Rt=ms\Delta T$
Specific heat of water is defined as the amount of heat required to increase the temperature of 1Kg water by${{1}^{\circ }}C$.
$s=4200\dfrac{j}{kg{{.}^{\circ }}C}$
$\Rightarrow {{7}^{2}}\times 60\times 60=40\times 4200\times \Delta T$
$\Rightarrow \Delta T=\dfrac{3600\times 49}{40\times 4200}$
$\Rightarrow \Delta T={{1}^{\circ }}C$

$\therefore$The rise in temperature of water due to coil in one minute is $\Delta T={{1}^{\circ }}C$ , option (1) is correct.

Additional information:
Water has a high specific heat capacity so increasing the temperature of water by one degree will require a high amount of energy which is due to the presence of so many hydrogen bonds in it.

Note:
There is a difference between heat capacity and specific heat capacity which causes confusion in solving heat transfer problems. Specific heat capacity is the heat required to raise a temperature of substance by one degree Celsius. But for heat capacity it is the ratio between the energy provided to substance and the increase in temperature with respect to it.