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Background:
suppose that we have single body say sphere and nothing else in the universe. Now it will radiate heat depending on its temperature.since its energy is going down its temperature will decrease.Eventually wel have energy in the form of photons and sphere at zero kelvin. thus In practical case, if we reduce the incoming radiation and increase the out going radiations by sutaibly choosing absorptivity and emissivity we will achieve heat transfer from body at lower temperature to body at higher temperature.
let us consider two infinite parallel plates P1 and P2 with vacuum in between them so that only radiation takes place between them
plate 2 is held at temperature t2.
Let us assume the following
Plate 1
Absorptivity a1 = 0.1
Emissivity e1 = 0.9
Temperature t1
Plate 2
abosrptivity a2 = 0.9
emissivity e2 = 0.1
Temperature t2
Then Consider a steady state
I claim that the steady state temperature of Plate 1 is not equal to t2
for steady state the Incoming heat on Plate 1 must be equal to outgoing heat.
Incoming heat = abosrptivity * radiation from plate 2
= 0.1 * 0.1* sigma* t2*t2*t2*t2 ---------equ1
where sigma is stefan Boltzmann constant = 5.67 exp(-8)
Outgoing heat = emissivity * BlackBody radiation at that temperature
= 0.9 * sigma * t1*t1*t1*t1 ------------ equ 2
Thus equating above 2 equations
0.1 * 0.1 * sigma t2*t2*t2*t2 = 0.9 *sigma *t1*t1*t1*t1
Thus we get
0.325 * t2 = t1
Thus if initially both bodies were at same temperature then more heat will leave plate 1 and thus cause cooling without any input of work.
this way we would be violating second law of Thermodynamics.
Note
It is observed that reflection effects cancel each other and are energy associated with reflection is quite low.
The materials with above mensioned properties are available.
we even considered spectral distribution of Emissivity and Absorptivity and found that overall emissivity or overall absorbtivity values of 0.1 or 0.9 can be obtained.
Final word
Can radiation effects violate second law of thermodynamics.
suppose that we have single body say sphere and nothing else in the universe. Now it will radiate heat depending on its temperature.since its energy is going down its temperature will decrease.Eventually wel have energy in the form of photons and sphere at zero kelvin. thus In practical case, if we reduce the incoming radiation and increase the out going radiations by sutaibly choosing absorptivity and emissivity we will achieve heat transfer from body at lower temperature to body at higher temperature.
let us consider two infinite parallel plates P1 and P2 with vacuum in between them so that only radiation takes place between them
plate 2 is held at temperature t2.
Let us assume the following
Plate 1
Absorptivity a1 = 0.1
Emissivity e1 = 0.9
Temperature t1
Plate 2
abosrptivity a2 = 0.9
emissivity e2 = 0.1
Temperature t2
Then Consider a steady state
I claim that the steady state temperature of Plate 1 is not equal to t2
for steady state the Incoming heat on Plate 1 must be equal to outgoing heat.
Incoming heat = abosrptivity * radiation from plate 2
= 0.1 * 0.1* sigma* t2*t2*t2*t2 ---------equ1
where sigma is stefan Boltzmann constant = 5.67 exp(-8)
Outgoing heat = emissivity * BlackBody radiation at that temperature
= 0.9 * sigma * t1*t1*t1*t1 ------------ equ 2
Thus equating above 2 equations
0.1 * 0.1 * sigma t2*t2*t2*t2 = 0.9 *sigma *t1*t1*t1*t1
Thus we get
0.325 * t2 = t1
Thus if initially both bodies were at same temperature then more heat will leave plate 1 and thus cause cooling without any input of work.
this way we would be violating second law of Thermodynamics.
Note
It is observed that reflection effects cancel each other and are energy associated with reflection is quite low.
The materials with above mensioned properties are available.
we even considered spectral distribution of Emissivity and Absorptivity and found that overall emissivity or overall absorbtivity values of 0.1 or 0.9 can be obtained.
Final word
Can radiation effects violate second law of thermodynamics.