An ideal gas in a cylindrical container of radius r and height h is kept at constant pressure p. the bottom of the container is maintained at temperature t0 while the top at temperature t1. assuming a linear temperature distribution along the cylinder, calculate the total mass of gas within the container.

Explanation:

The gas ideal law is  

PV= nRT (equation 1)

Where:

P = pressure  

R = gas constant  

T = temperature  

n= moles of substance  

V = volume  

Working with equation 1 we can get  

The number of moles is mass (m) / molecular weight (mw). Replacing this value in the equation we get.

 or  

  (equation 2)

The cylindrical container has a constant pressure p  

The volume is the volume of a cylinder this is

Where:

r = radius  

h = height  

(pi) = number pi (3.1415)

This cylinder has a radius, r and height, h so the volume is  

Since the temperatures has linear distribution, we can say that the temperature in the cylinder is the average between the temperature in the top and in the bottom of the cylinder. This is:  

Replacing these values in the equation 2 we get:

  (equation 2)

a rain shadow is a dry region of land on the side that is protected against the prevailing winds of a mountain range. the prevailing winds are the winds that occur most of the time in a particular place of the earth

prevailing winds carry air toward the mountain range. as the air rises up over a mountain range, the air cools, water vapor condenses, and clouds form. on this side of the mountains, called the windward side, precipitation falls in the form of  rain  or snow. this dry air produces a  rain shadow.