UNIVERSAL GAS LAW
The universal gas law is a combination ofBoyle’s law and Charles’ law. It states that the product of the initial pressure, initial volume, and new temperature (absolute scale) of an enclosed gas is equal to the product of the new pressure, new volume, and initial temperature. The formula is as follows:
PVT´ = P´ V´ T
P = intitial pressure
V = initial volume
T = initial temperature (absolute)
P´ = new pressure
V = new volume
T = new temperature (absolute)
For example, assume the pressure of a 500cm3volume of gas is 600 mb and the temperature is 30°C (303° absolute). If the temperature is in-creased to 45°C (318° absolute) and the volume is decreased to 250 cm3, what will be the new pressure of the volume? Applying the formula, we have
P = 600 mb
V = 500 cm3
T = 303°K
EQUATION OF STATE
The equation of state is a general gas law forfinding pressure, temperature, or density of a dry gas. Rather than using volume, this formula uses what is called gas constant. A gas constant is a molecular weight assigned to various gases. Ac-tually, air does not have a molecular weight be-cause it is a mixture of gases and there is no such thing as an air molecule. However, it is possible to assign a so-called molecular weight to dry air that makes the equation of state work. The gas constant for air is 2,870 and for water vapor it is 1,800 when the pressure is expressed in millibars and the density is expressed in metric tons per cubic meter. The gas constant may be expressed differently depending on the system of units used. The following formula is an expression of the equation of state:
P = pressure in millibars
= density (Greek letter rho) R = specific gas constant T = temperature (absolute) The key to this formula is the equal sign that
P = pressure in millibars
= density (Greek letter rho)
R = specific gas constant
T = temperature (absolute)
The key to this formula is the equal sign thatseparates the two sides of the formula. This equal sign means that the same value exists on both sides; both sides of the equation are equal. If the left side of the equation (pressure) changes, a cor-responding change must occur on the right side (either in the density or temperature) to make the equation equal again. Therefore, an increase of the total value on one side of the Equation of State must be accompanied by an increase of the total value on the other side. The same is true of any decrease on either side.
NOTE: Since R is a constant it will always remain unchanged in any computation. The right side of the equation can balance out any change in either density or temperature without having a change on the left side (pressure). If, for example, an increase in temperature is made on the right side, the equation maybe kept in balance by decreasing density. This works for any value in the equation of state.
From this relationship, we can draw the following conclusions:
1. A change in pressure, density (mass or volume), or temperature requires a change in one or both of the others.
2. With the temperature remaining constant, an increase in density results in an increase in at-mospheric pressure. Conversely, a decrease in density results in a decrease in pressure.
NOTE: Such a change could occur as a result of a change in the water vapor content.
3. With an increase in temperature, the pressure and/or density must change. In the free atmosphere, a temperature increase frequently results in expansion of the air to such an extent that the decrease in density outweighs the temperature increase, and the pressure actually decreases. Likewise, a temperature increase allows an increase in moisture, which in turn decreases density (mass of moist air is less than that of dry air). Couple this with expansion resulting from the temperature increase and almost invariably, the final result is a decrease in pressure.
At first glance, it may appear that pressure increases with an increase in temperature. Earlier, however, it was noted that this occurs when volume (the gas constant) remains constant. This condition would be unlikely to occur in the free atmosphere because temperature increases are associated with density decreases, or vice versa. The entire concept of the equation of state is based upon changes in density rather than changes in temperature.