Question

In Joule’s Calorimeter experiment, when a current of $1$ Ampere is passed through a coil for a known interval of time ‘t’, the temperature of water increases from ${30}^{\circ }C$to ${33}^{\circ }C$. When a current $2A$ is passed through the same coil placed in the same quantity of water and for the same time, the temperature of water increases from ${30}^{\circ }C$ to,
$A.{33}^{\circ }C$
 $B.{36}^{\circ }C$
$C.{39}^{\circ }C$
$D.{42}^{\circ }C$

Answer 1

Hint:A Calorimeter is a device used to measure the amount of heat involved in a chemical or physical process. For example, when an exothermic reaction occurs in a calorimeter, the heat produced by the reaction is absorbed by the solution, which increases its temperature. The principle of Calorimeter indicates the law of conservation of energy.

Formulae Used: We will be using the relation of$1$) Heat is related to the rise in temperature$H=mcdT$ and $2$) Joule’s equation of electrical heating $H=i^{2}Rt$

Complete step by step answer:
When a resistor absorbs electrical energy, it dissipates the energy in the form of heat H. If the resistor is placed in the calorimeter, the amount of heat produced can be measured when it is absorbed in the calorimeter. The heat Q produces a temperature rise $dT$. The resistor coil is immersed in the water in a calorimeter. The heat Q produces a temperature rise $dT$. The heat is related to $dT$
The heat generated in water that resulted in the temperature of water increases from ${30}^{\circ }C$to ${33}^{\circ }C$ is given by,
$H=mcdT$
Where m is the mass of water
$dT=$ $$(33-30)=3$$ is the temperature difference.
Current passed through the coil, $i_1=1A$
Therefore H is equal to $i^{2}Rt$
Where, i, R, and t are the current, resistance of the coil, and temperature respectively.
$\Rightarrow i^{2}Rt=mcdT$
Here R, t, C, and m remain the same, but current increased to$i_2=2A$
Hence, $i_2^2=mcd{T}^{\prime }$
Dividing the two equations,
${\displaystyle \frac{d{T}^{\prime }}{dT}}={\displaystyle \frac{2^2}{1^2}}$ $${(}^{\circ }C)$$
$d{T}^{\prime }=12$
Therefore, the final temperature$=30+12={42}^{\circ }C$

 Option $$D)$$ ${42}^{0}C$

Note:A Calorimeter is a device used to measure the amount of heat involved in a chemical or physical process. For example, when an exothermic reaction occurs in a calorimeter, the heat produced by the reaction is absorbed by the solution, which increases its temperature. The principle of Calorimeter indicates the law of conservation of energy.