A copper wire has a resistance of 0.425 Ω at 20.0°C, and an iron wire has a resistance of 0.443 Ω at the same temperature. At what temperature are their resistances equal? The temperature coefficient of resistivity for copper is 3.90 10-3(°C)−1 and for iron it is 5.00 10-3(°C)−1.

Their resistances equal at - 12.29°C.

Explanation:

given information:

copper wire's resistance, Ω

iron wire's resistance Ω

coefficient resistivity of copper, αc = 3.90 x 10⁻³ /°C

coefficient resistivity of iron, αi = 5.00 x 10⁻³ /°C

Resistance  at any temperature is

R = [1 + α ΔT], ΔT =

where

R = the resistance of the conductor at the temperature "T"

= conductor resistance at reference temperature

α =  coefficient of resistivity of conductor

T = Temperature

= temperature reference, usually 20°C

At what temperature are their resistances equal?

[1 + αc ΔT] = [1 + αi ΔT]

0.425 [1 + 3.90 x 10⁻³ΔT] = 0.443 [1 + 5.00 x 10⁻³ΔT]

0.425 + 1.6575 x 10⁻³ΔT = 0.443 + 2.215 x 10⁻³ΔT

- 0.018 = 0.5575 10⁻³ ΔT

ΔT = - 32.29°C

ΔT = T -

T = ΔT +

  = - 32.29 + 20

  = - 12.29°C

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.