In this clip I will give you a brief overview of one of the fundamental laws concerning the atmosphere the ideal gas law
for any gas or mixture of gases the pressure within a given volume is determined by the temperature and the number of molecules in that volume.
From this we have a God rose hypothesis. If two gases in this case gas a and a gas B. have the same pressure P. the same temperature T. and are confined to two identical volumes V. then these two gases consist of exactly the same number of molecules and note that even if the molecules are completely different this hypothesis still applies. For any gas there are three quantities pressure temperature and volume that we use to describe what we call the state of the gas. Therefore these three quantities are called the state variables they tell us something about the state that a gas is in
the fundamental equation of state also known as the ideal gas law combines these three quantities. The constant in this equation depends on the number of gas molecules
three other laws can be derived from the equation of state.
If we keep the volume constant then the equation of state can be simplified into the law of gay Lu sac. Which states that if the temperature increases then the pressure has to increase proportionally.
If we keep the temperature constant then we have Boyle's Law which states that if we compress the gas thereby decreasing the volume.
Then the pressure must increase Finally if we keep the pressure constant then we have Charles's law which states that if we heat the gas then its value must increase
in order to calculate the constant in the gas law we assume that we have one kill a mole of gas that is to say that we have an A number of molecules which is called a God or is number.
We can also assume that the standard values for temperature and pressure apply.
Given these conditions any gas will occupy the volume of twenty two point four one four cubic meters the standard Moeller volume
with these values we can calculate the constant. This is the quantity our star also called the universal gas constant. This is the constant in the gas law if we have exactly one kilo mole of gas
we can rearrange the equation of state as follows
If the amount of gas is an.
We have to multiply our star by N.. We know that the mass M. of and kilometers of gas equals N. multiplied by capital M.. Where capital M. is the molar mass of the gas
combining these last two equations result in P. multiplied by V. is equal to M. multiplied by R. and T.. Where the universal gas constant are star has been replaced by the specific gas constant R. It is called specific because R. is no longer universal but instead depends on the sort of gas that we are dealing with
the are for oxygen for example would be different than they are for ninth region or they are for ozone or the are for any other gas.
An alternative and often used form of the gas law can be derived when we realize that density is mass divided by volume
which leads to the expression on the right which is commonly used for the gas law in reality density is difficult to measure but with the help of the gas law density can be easily calculated
humid air is a mixture of dry air and water vapor dry air itself is a mixture with almost constant proportions of nitrogen and oxygen as well as many other gases. But the amount of water vapor is highly variable.
Now we can apply Dalton's law which states that the total pressure of a mixture of gases is simply the sum of the so-called partial pressures of the various gases in the mixture so if gas a exert a partial pressure P. A and gas B. exerts a partial pressure P. B. then the total pressure is simply the sum of P. A plus P. B. for humid air we have dry air with a partial pressure P. D. where the D. stands for dry and water vapor with a partial pressure.
The total pressure is the sum of these two variables
because molecules of dry air are not influenced by molecules of water vapor dry air would behave exactly the same with or without water molecules This means that for dry air the gas law is given by this expression. Where all indices D. refer to dry air. The specific gas constant for dry air can be calculated from the universal gas constant Our star and the average molar mass of air am D..
In turn water molecules behave as if the air molecules did not exist it means that they obey their own gas law. Were all indices v referred to vapor water vapor that is. And the specific gas constant for water vapor can be calculated in a similar manner as before
the gas law for human hair can now be derived using Dalton's equation and the two gas laws for dry air and water vapor we won't show you this specific of how the equation is derived but it results in an equation where P. is the total pressure of the humid air at temperature T. Rowe is the density and R. M. the specific gas constant from waste air however this expression is never used. Instead we use our D. and put all of the information concerning the varying amounts of water vapor into the temperature.
In the equation T.V. is called the Virtual temperature.
And its value depends on the real temperature T. as well as the amount of water vapor.
The concept of the virtual temperature can be better understood if we compare of volume of humid air to a volume of dry air suppose that initially the pressure temperature and volume for both is exactly the same. If this is the case the density of the humid air would be less than the density of the dry air this is because humid air contains a number of relatively light water vapor molecules whereas dry air contains relatively heavy air molecules.
We will now adapt the volume of the dry air box in such a way that the density ro prime D. will be the same as the density of the humid air.
Because dry air is heavier the volume has to increase.
When using the ideal gas law this can only happen if the temperature increases as well otherwise the pressure would drop. The higher temperature of the dry air when the densities of the humid air and dry air are equal is called the Virtual temperature T.V..