COMEDK 2023 Shift 1 Paper

The thermal power radiated by a black body is given by Stefan's law, according to which the power radiated (P) is directly proportional to the fourth power of the absolute temperature (T) of the body. This can be mathematically expressed as:
P=σeAT4
where:
σ is the Stefan-Boltzmann constant,
e is the emissivity of the surface,
A is the surface area,
T is the absolute temperature in Kelvin.
For the given problem, since both black bodies have equal surface areas and are perfect black bodies (assuming e=1 for both), the ratio of their thermal powers PP to PQ can be simplified to the ratio of the fourth powers of their absolute temperatures. To work with absolute temperatures, we must first convert the given Celsius temperatures to Kelvin:
Temperature of P=127∘C=127+273=400K
Temperature of Q=27∘C=27+273=300K
The ratio of their thermal powers can thus be expressed as:
‌

Pp

PQ

=‌

σ×A×(400)4

σ×A×(300)4

Simplifying this, we get:
‌

Pp

PQ

=‌

(400)4

(300)4

=(‌

4

3

)4
Calculating the power of 4 :
‌

Pp

PQ

=(‌

44

34

)=‌

256

81

Therefore, the correct option is:
Option D 256:81.