A cup of coffee with temperature 155degreesF is placed in a freezer with temperature 0degreesF. After 15 minutes, the temperature of the coffee is 46degreesF. Use Newton's Law of Cooling to find the coffee's temperature after 20 minutes.

= 30.67°F

 ≅ 30.70°F

Explanation:

Newton's law,

When T(t) is the final temperature

= Temperature of surrounding

= Initial temperature

=duration of cooling

k = constant

Now take natural log on both the sides

k = 0.081

  = 155 (0.1979)

 = 30.67°F

 ≅ 30.70°F

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.