Question

The figure shows a radiant energy spectrum graph for a black body at a temperature $ T $ , if the temperature of the body is raised to a higher temperature $ T' $ , then choose the correct statement (s):

(A) The intensity of radiation for every wavelength increases.
(B) The maximum intensity occurs at a shorter wavelength.
(C) The area under the graph increases.
(D) The area under the graph is proportional to the fourth power of temperature.

Answer 1

Hint :To solve this question we have to understand the concept and phenomenon of black body radiation and consider each and every point of the radiation so that we can find the correct statement for this graph shown in figure. This graph shows all the concepts of black body radiations.

Complete Step By Step Answer:
Let us first understand the concept of black body radiation and its phenomenon.
Black body is one which absorbs totally all the radiations of any wavelength which fall on it. The main characteristics of such a body is that when heated to a suitable high temperature it emits full or total radiation. As it is a perfect absorber it is also a perfect radiator, its emission being the greatest possible for every wavelength at any given temperature.
The radiant energy spectrum of black body radiations shows:
Let us consider some temperatures in increasing order
 

In the above diagram we can observe the intensity of radiation for every temperature. Also, area increases as the intensity increases at a given temperature. The total energy of radiation at any temperature is given by the area between the curve corresponding to that temperature and the horizontal axis. The area is found to be proportional to fourth power of the corresponding absolute temperature. It is stated in Stefan’s law of radiation.
Hence, we have reached the correct answer for this question that option A, C and D are correct options.

Note :
 Here, it has been discussed that the energy intensity increases with increase in temperature. Area under the curve increases with increase in temperature. These are the laws of black body radiation named after different scientists after the observation of black body at different wavelengths at different temperatures. To know more, study all the laws namely Wein’s law, Stefan’s law and Rayleigh-Jeans law.