What temperature is required to transfer waste heat to the environment for a heat engine to be 100 percent efficient?

An infinite temperature

Explanation:

The efficiency of an engine is defined as:

where

is the temperature at which heat enters the engine

is the temperature of the environment, to which the engine exhausts heat

From the formula, we see that for an engine to be 100% efficient, the fraction

must be equal to zero. Since the value of is never zero (the temperature is expressed in Kelvin, and the temperature of the environment can never be exactly 0 K), the only possibility for that to occur is that the temperature at which heat enters the engine () is infinite, so that this fraction becomes zero and the efficiency becomes 1.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

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