Evangelista Torricelli was the first person to realize that we live at the botto

Question

Evangelista Torricelli was the first person to realize that we live at the bottom of an ocean of air. He correctly surmised that the pressure of our atmosphere is attributable to the weight of the air. The density of air at 0°C at the Earth's surface is 1.29 kg/m3. The density decreases with increasing altitude (as the atmosphere thins). On the other hand, if we assume that the density is constant at 1.29 kg/m3 up to some altitude h, and zero above that altitude, then h would represent the depth of the ocean of air.

(a) Use this model to determine the value of h that gives a pressure of 1.00 atm at the surface of the Earth.

(b) Would the peak of Mt. Everest rise above the surface of such an atmosphere?

Yes or no?

Explanation / Answer

According to the problem,

Conventional approach to derive atmospheric pressure at the surface of the earth by mercury barometer:

P = h**g

= 0.76*13.6*10^3*9.8
= 1.01 * 10^5 pa or N/m^2
= 1 atm pressure

a)According to model given,

Pressure at the bottom i.e at surface = 1 atm = 10^5 pa

Again Using the same expression,

P = h**g

10^5 = h*1.29*9.81 [=density of air]

h = 10^5/(1.29*9.81)

h = 7910.14 m The height of the ocean of air approx comes around 8 km.

b)No, it does not

Explanation: The earth's atmosphere consists of several layers and extends far away from the earth out to 10,000 km. The lowest layer of the earth's atmosphere is the Troposphere, which extends to about 17 km above the surface at the equator. This is almost double the height of Mt. Everest, so the mountain is WELL within the atmosphere.

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