1. Variations in DensityPerhaps you have wondered how much air
weighs. The air around you has a particular density, and any volume of
air contains a certain amount of mass. Changes in the density of air
affect many everyday phenomena. For example, the density of the
atmosphere influences how much lift a plane gets as it accelerates down a
runway in preparation for takeoff. Likewise, automobile fuel injectors
must account for variations in density to deliver the right mixture of
gasoline and air into the car’s engine. The density of air can even
affect the amount of resistance the air exerts on a batted baseball,
thereby influencing its distance traveled.Effect of Temperature on
DensityBut are the variations in density really substantial? We can use
the equation of state to see exactly how much variations in temperature
affect the air’s density. To do this, let’s first rearrange the equation
to the following:...Let’s now also compare the air density for two
situations: a warm day with a temperature of 308 K (35 °C or 95 °F) and a
cold one with a temperature of 278 K (5 °C or 41 °F). For consistency,
we will assume that the pressure is 100,000 Pa (1000 mb; 100
kilopascals) in both instances.Applying the equation of state for the
warmer day, we find that the density of the air is...When we lower the
air temperature to 278 K (5 °C or 41 °F), the equation yields an air
density of...This is nearly 11 percent greater than the density the air
had on the warmer day—a nontrivial amount.Effect of Humidity on
DensityIn addition to temperature and pressure, the humidity of the air
exerts an influence (although only a very minor one) on density. Let’s
see how. Molecular oxygen (O2) and nitrogen (N2) make up most of the
mass of the atmosphere and exist in a constant proportion. Other, lesser
constituents of the atmosphere are present in different amounts at
different places and times, and because each has its own unique
molecular weight (an expression of the relative amount of mass for
molecules), their relative abundance can slightly affect the density of
the atmosphere. Among these gases, water vapor usually accounts for
about 1 percent of the atmospheric mass. Intuitively, we might assume
that a greater humidity would favor a denser atmosphere. Actually, just
the opposite is true.Compare the amount of mass contained in individual
molecules of water vapor and of the most abundant atmospheric gases. The
molecular weights of nitrogen and oxygen are 28.01 and 32.00,
respectively, and the mean molecular weight of the dry atmosphere is
28.5. Water vapor, on the other hand, has a molecular weight of only
18.01. Thus, as the proportion of the air occupied by water vapor
increases, an accompanying reduction in the mean molecular weight of the
atmosphere must occur. All other things being equal, humid air is less
dense than dry air.Incorporating the effect of varying moisture content
requires only a small modification to the equation of state.
Calculations using the revised formula show that at 15 °C (59 °F), air
density declines by only 0.6 percent for a 1 percent increase in water
vapor (from dry air to 1 percent water vapor).Why is humid air less
dense than dry air at the same temperature and pressure? Get solution
2. Variations in DensityPerhaps you have wondered how much air weighs. The air around you has a particular density, and any volume of air contains a certain amount of mass. Changes in the density of air affect many everyday phenomena. For example, the density of the atmosphere influences how much lift a plane gets as it accelerates down a runway in preparation for takeoff. Likewise, automobile fuel injectors must account for variations in density to deliver the right mixture of gasoline and air into the car’s engine. The density of air can even affect the amount of resistance the air exerts on a batted baseball, thereby influencing its distance traveled.Effect of Temperature on DensityBut are the variations in density really substantial? We can use the equation of state to see exactly how much variations in temperature affect the air’s density. To do this, let’s first rearrange the equation to the following:...Let’s now also compare the air density for two situations: a warm day with a temperature of 308 K (35 °C or 95 °F) and a cold one with a temperature of 278 K (5 °C or 41 °F). For consistency, we will assume that the pressure is 100,000 Pa (1000 mb; 100 kilopascals) in both instances.Applying the equation of state for the warmer day, we find that the density of the air is...When we lower the air temperature to 278 K (5 °C or 41 °F), the equation yields an air density of...This is nearly 11 percent greater than the density the air had on the warmer day—a nontrivial amount.Effect of Humidity on DensityIn addition to temperature and pressure, the humidity of the air exerts an influence (although only a very minor one) on density. Let’s see how. Molecular oxygen (O2) and nitrogen (N2) make up most of the mass of the atmosphere and exist in a constant proportion. Other, lesser constituents of the atmosphere are present in different amounts at different places and times, and because each has its own unique molecular weight (an expression of the relative amount of mass for molecules), their relative abundance can slightly affect the density of the atmosphere. Among these gases, water vapor usually accounts for about 1 percent of the atmospheric mass. Intuitively, we might assume that a greater humidity would favor a denser atmosphere. Actually, just the opposite is true.Compare the amount of mass contained in individual molecules of water vapor and of the most abundant atmospheric gases. The molecular weights of nitrogen and oxygen are 28.01 and 32.00, respectively, and the mean molecular weight of the dry atmosphere is 28.5. Water vapor, on the other hand, has a molecular weight of only 18.01. Thus, as the proportion of the air occupied by water vapor increases, an accompanying reduction in the mean molecular weight of the atmosphere must occur. All other things being equal, humid air is less dense than dry air.Incorporating the effect of varying moisture content requires only a small modification to the equation of state. Calculations using the revised formula show that at 15 °C (59 °F), air density declines by only 0.6 percent for a 1 percent increase in water vapor (from dry air to 1 percent water vapor).The worked example showed a density difference of 0.13 kg/m3 over a temperature change of 20 °C. Suppose the example had compared temperatures 40 °C apart. Would the density difference be twice as large? Get solution
2. Variations in DensityPerhaps you have wondered how much air weighs. The air around you has a particular density, and any volume of air contains a certain amount of mass. Changes in the density of air affect many everyday phenomena. For example, the density of the atmosphere influences how much lift a plane gets as it accelerates down a runway in preparation for takeoff. Likewise, automobile fuel injectors must account for variations in density to deliver the right mixture of gasoline and air into the car’s engine. The density of air can even affect the amount of resistance the air exerts on a batted baseball, thereby influencing its distance traveled.Effect of Temperature on DensityBut are the variations in density really substantial? We can use the equation of state to see exactly how much variations in temperature affect the air’s density. To do this, let’s first rearrange the equation to the following:...Let’s now also compare the air density for two situations: a warm day with a temperature of 308 K (35 °C or 95 °F) and a cold one with a temperature of 278 K (5 °C or 41 °F). For consistency, we will assume that the pressure is 100,000 Pa (1000 mb; 100 kilopascals) in both instances.Applying the equation of state for the warmer day, we find that the density of the air is...When we lower the air temperature to 278 K (5 °C or 41 °F), the equation yields an air density of...This is nearly 11 percent greater than the density the air had on the warmer day—a nontrivial amount.Effect of Humidity on DensityIn addition to temperature and pressure, the humidity of the air exerts an influence (although only a very minor one) on density. Let’s see how. Molecular oxygen (O2) and nitrogen (N2) make up most of the mass of the atmosphere and exist in a constant proportion. Other, lesser constituents of the atmosphere are present in different amounts at different places and times, and because each has its own unique molecular weight (an expression of the relative amount of mass for molecules), their relative abundance can slightly affect the density of the atmosphere. Among these gases, water vapor usually accounts for about 1 percent of the atmospheric mass. Intuitively, we might assume that a greater humidity would favor a denser atmosphere. Actually, just the opposite is true.Compare the amount of mass contained in individual molecules of water vapor and of the most abundant atmospheric gases. The molecular weights of nitrogen and oxygen are 28.01 and 32.00, respectively, and the mean molecular weight of the dry atmosphere is 28.5. Water vapor, on the other hand, has a molecular weight of only 18.01. Thus, as the proportion of the air occupied by water vapor increases, an accompanying reduction in the mean molecular weight of the atmosphere must occur. All other things being equal, humid air is less dense than dry air.Incorporating the effect of varying moisture content requires only a small modification to the equation of state. Calculations using the revised formula show that at 15 °C (59 °F), air density declines by only 0.6 percent for a 1 percent increase in water vapor (from dry air to 1 percent water vapor).The worked example showed a density difference of 0.13 kg/m3 over a temperature change of 20 °C. Suppose the example had compared temperatures 40 °C apart. Would the density difference be twice as large? Get solution
