Question

Give reason: we prefer white clothes in summer and dark clothes in winter.

Answer 1

To understand why we prefer white or one can say brighter clothes in summer and dark clothes in winter, we need to first understand the properties of these different colors under different parameters. That is how they react to change in temperature around us, how they react with light and etc.

Complete answer:
Now, from the property of a black body. We can say that the amount of heat absorbed by a particular color depends on certain parameters. We will understand this mathematically. For that, let us first assign some terms that we are going to use.
Let the absolute emissivity of the object be given by ‘e’.
Let the temperature of the surrounding be denoted by ‘T’.
And, let the surface area of the object emitting all this radiation be ‘A’.
Then, the radiation power emitted by the object is found to be proportional to:
$\begin{aligned} & \Rightarrow E\propto e \\\ & \Rightarrow E\propto A \\\ & \Rightarrow E\propto {{T}^{4}} \\\ \end{aligned}$
Thus, on combining these equations, we get:
$\Rightarrow E\propto eA{{T}^{4}}$
Or, $\Rightarrow E=\sigma eA{{T}^{4}}$ [Let this expression be equation number (1)]
Where, $\sigma$ is the proportionality constant also known as Stefan-Boltzmann constant.
From equation number (1), we can see that power radiated is proportional to ‘e’.
Now, for a black body or one can say a dark body, ‘e’ is close to 1. That is, such a type of body is a good radiator.
But, an interesting fact about radiation is that, if a body is a good radiator it is as good of an absorber. Thus, a dark or black body will absorb too much heat as compared to a light colored body.
This is the main reason why we wear light clothes in summer as they are bad absorbers of heat and wear dark clothes in winter as they are good absorbers of heat.

Note:
We should always try to avoid wearing dark clothes in summer and try to wear bright clothes in summer and do the opposite in winter, as there is a significant difference in the amount of heat absorbed. This is because the whole term is multiplied by temperature to its fourth power, which brings the significant change.