Boyle’s law states that when a sample of gas is compressed at a constant temperature, the pressure p of the gas is inversely proportional to the volume v of the gas. (a) suppose that the pressure of a sample of air that occupies 0.106 m3 at 25°c is 50 kpa. write v as a function of p. (b) calculate dvydp when p − 50 kpa. what is the meaning of the derivative? what are its units?

a)

b).

Explanation:

Given that

Boyle's law

P V = Constant ,at constant temperature

a)

Given that

We know that for PV=C

Now by putting the values

PV= 50 x 0.106

Where P is in KPa and V is in

b)

PV= C

Take ln both sides

So

lnP + lnV =lnC               ( C is constant)

By differentiating

So

When P= 50 KPa

It indicates the slope of PV=C curve.

It unit is .

Or we can say that .

increases it

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.