Question

If the sun becomes twice hotter, it will radiate,
A) Energy sixteen times larger.
B) Predominantly in the infrared.
C) Predominantly in the ultra violet.
D) Energy sixteen times smaller.

Answer 1

Hint
The Stefan’s Boltzmann law is given by $E = \sigma eA{T^4}$. Sun would become twice hotter means temperature will become twice and hence the energy will become 16 times.

Complete step by step answer
The total energy which is emitted per second per meter square by a blackbody at a given temperature is proportional to the fourth power of its absolute temperature. This relationship is known as the Stefan-Boltzmann Law.
The law is given by the formula,
$E = \sigma eA{T^4}$
Where E is the total energy.
$\sigma $ is the stefan’s constant whose value in Si units is $5.67 \times {10^{ - 8}}J{s^{ - 1}}{m^{ - 2}}{K^{ - 4}}$.
A is the surface area of the black body.
e is the emissivity.
T is the temperature.
Now since the sun is becoming twice hotter, it would mean that the temperature of the sun has been doubled. It is clear from the above expression that if temperature doubles, then total Energy will become 16 times.
Mathematically,
${E'} = \sigma eA{(2T)^4}$
Hence
$\Rightarrow {E'} = 16\sigma eA{(T)^4} $
$\Rightarrow {E'} = 16E $
So, the energy becomes 16 times and hence option (A) is the correct answer.

Note
The hotter is the object, the shorter is the wavelength of the radiation it emits. And the hotter temperatures, more energy is emitted at all wavelengths. But the peak amount of energy is radiated at shorter wavelengths for higher temperatures. This relationship is known as Wien’s Displacement Law.