Question

If the same amount of milk and water are kept in two beakers and heated on the two burners of a gas by supplying equal amounts of heat. Despite this,why is the rise in temperature of milk more than that of water?

Answer 1

Hint: Here we need to look at what factors the rise of temperature of a body depends. Then we will be able to determine the cause of different increases in temperature for different liquids while the same amount of heat is supplied to them.We will follow these steps to solve the problem.

Formula used: $H=Ms\vartriangle t$

Complete step by step solution: If $H$ is the amount of heat supplied to a body of mass $M$ having the specific heat of the material $s$ and if due to this amount of heat the change in temperature of the body is $\vartriangle t$ ,then we have
$H=Ms\vartriangle t$. Let specific heat of water is ${{s}_{w}}$ and that of milk is ${{s}_{m}}$ .Now ${{s}_{w}}=1ca\operatorname{l}/gm{}^{0}C$ and ${{s}_{m}}=0.6cal/gm{}^{0}C$ ,thus ${{s}_{w}}>{{s}_{m}}$ . Now if $H$ amount of heat is supplied to both of them having the same mass $M$ and the rise in temperature of water and milk are $\vartriangle {{t}_{w}}$ and$\vartriangle {{t}_{m}}$ respectively then we can write
$H=M{{s}_{w}}\vartriangle {{t}_{w}}...........(1)$ and
$H=M{{s}_{m}}\vartriangle {{t}_{m}}...........(2)$
Dividing $(2)$ by $(1)$ we get
$\begin{align}
  & \dfrac{H}{H}=\dfrac{M{{s}_{m}}\vartriangle {{t}_{m}}}{M{{s}_{w}}\vartriangle {{t}_{w}}} \\
 & or\dfrac{\vartriangle {{t}_{m}}}{\vartriangle {{t}_{w}}}=\dfrac{{{s}_{w}}}{{{s}_{m}}}>1 \\
\end{align}$
Because ${{s}_{w}} > {{s}_{m}}$
So the temperature rise of milk will be higher as the specific heat of water is greater than the specific heat of milk.

Note:
The rise in temperature depends on the amount of heat supplied, mass of the body as well as on the specific heat of the material. In this problem the heat supplied and mass in both the cases are equal. So rise in temperature only depends on the specific heats of the two substances. If the other parameters are also changing then we have to consider them as well. Also we need to put the values of all the quantities in the same system of units.