Temperature Thermometers The Ideal Gas Relation - Pressure, Temperature, and Density
Temperature
As we have learned, temperature is a measure of the average speeds of the atoms and molecules that make up an object or substance.
Temperature measurements - thermometers
A thermometer is an instrument used to measure temperature. There are basically two types of thermometers - mercurial and electronic (digital). They both work in different manners.
A mercurial thermometer works by properties of thermal expansion. Most substances in the universe expand upon being heated and contract upon being cooled. This principle is employed in mercury thermometers. Mercury is inserted into a narrow g lass shaft at a given temperature. Then it is calibrated numerically. As the air cools or heats, the mercury responds accordingly.
One of the definite advantages of using mercury is its low freezing point. If another substance, such as water, were employed, it would freeze at 32 F and low temperature measurements would be impossible.
Another type of thermometer is the electronic thermometer. It works through principles of electrical resistivity. Resistance is the amount of current that is lost as electricity flows through a conductor, such as copper.
In an electronic thermometer, a current is continuously being sent between two electrodes and a resistor is placed between them. Electrical resistivity is a function of temperature - the higher the temperature, the higher the resistivity. The power t hat is lost in the resistor through resistivity is lost in the form of heat. That heat energy heats up an electrode cell which then is calibrated digitally to display the temperature.
These types of thermometers are often accurate to the nearest .001 degrees and are employed in cars, aircraft, and most other industrial and commercial uses.
Infrared satellite photography to estimate temperature
As we have learned, all matter that has a temperature above absolute zero emits energy as a function of the fourth power of its temperature. The higher the temperature of an object, the more energy it will emit (recall this is called the Stefan-Bol tzman Law). To take advantage of this principle, scientists employ infrared satellite pictures. Satellites in space take measurements of the amount of infrared energy that different parts of the world are emitting. Through the use of compute rs, the amount of infrared energy can be calibrated according to temperature. To better visually understand a temperature distribution, different energy levels will be converted into colors - red usually being coldest.
Night vision cameras and other similar instruments employ this principle of energy emittance as a function of temperature.
Pressure
Pressure and temperature are closely related. At a microscopic level, the pressure of a gas can be defined as a function of the number of collisions that molecules make with a surface in a given time period. More accurately, it is the amount of energ y imparted on an open surface.
At a macroscopic level, pressure can be defined as the amount of force per unit area.
The pressure of a gas is directly related to its temperature. Let us consider that from a visual point of view:
Suppose we have a container that is filled with a fixed number of molecules. There will be a given number of collisions with the sides of the container from the molecules in a given amount of time. Let's suppose we increase the temperature. The spee ds of the molecules will increase, thus in that same time period, there will be more collisions with the walls and more energy imparted, thus the pressure will increase.
Density
Density is defined as the amount of matter that will fit into a given volume. Volume refers to the amount of space that a given sample of matter occupies. Volume is a 3-dimensional quantity. We refer to a length, width, and height when we consider t he volume of a cube for instance. Mathematically, density is defined as mass divided by volume and is often represented by the Greek symbol, rho.
The density of water is 1000 kg/m^3, or 62.4 lbs/ft^3. That means that suppose I have a box that is one cubic foot. 62.4 pounds of water will fit inside of it.
The average density of air on the surface of Earth is around 1.25 kg/m^3. 1.25 kilograms of air will fit into a cubic meter of air.
Density is proportional to temperature and pressure. Let us consider that same container that we considered above when we discussed pressure. If we were to increase the density, that would mean we would need to increase the amount of mass in the cont ainer since density is mass divided by volume. Since our container will not change in size, the mass will need to increase for the density to increase. To do this, we will need to add more molecules. Adding more molecules will increase the number of mo lecular collisions with the sides of the container thus increasing the pressure. Also, the amount of collisions between molecules will increase, thus adding more energy to the system and increasing the average kinetic energies (thus velocities) of the mo lecules thus increasing the temperature.
The Ideal Gas Expression
There is an equation that describes how temperature, pressure, and density are related. It is often expressed as:
The Gas Constant, symbolized R, is called the Universal Gas Constant. The wonderful aspect of this equation is that it behaves very accurately no matter which gas you are considering: air, carbon dioxide, neon, or anything else.
The Ideal Gas Expression can be employed for mass densities or molar densities. A mole is 6.02 * 10^23 of anything. Chemists, scientists, and engineers often deal with molecular quantities in terms of the number of moles. A mole of water molecules for instance, weighs 18 grams.
A molar density is the number of moles of a given substance that will fit into a given volume. A mass density as discussed earlier, is the amount of mass of a given substance that will fit into a given volume.
The molar form of the Ideal Gas Expression can be represented as:
We can show mathematically with the assistance of the Ideal Gas Expression what we discussed visually above in terms of the relationships between pressure, volume, and temperature.
The Ideal Gas Expression is an extremely important fundamental equation in the study of meteorology and will be referred to frequently throughout the semester so please make sure you spend some time considering it and making sure you understand its bas ic concept.
Atmospheric pressure
As we will learn in the coming weeks, the atmosphere's pressure plays an extremely important role in determining the weather. Variations in pressure drive the wind. To illustrate the basic concept behind wind we will consider a pressure gradient. (A gradient is a change in a given quantity over a change in a given distance - will be discussed at length in class).
Consider our container. Suppose initially we have twice as many molecules on the left side of the container as the right side. Intuitively, we can reason that the pressure on the left side is twice that on the right side and we can further show that with the aid of the Ideal Gas Expression. The system will strive to get to equilibrium such that the density throughout the container is uniform. In order for this to occur, there must be a transfer of molecules from the left toward the right. T his basic concept, applied to the much larger scale of the atmosphere, is the basis for wind.
Earth's pressure on average is around 14.7 pounds/square inch. That means if you were to take a one inch by one inch square on the Earth's surface and extend it up to the edge of space, that column would weigh about 14.7 pounds.
Meteorologists, scientists, and engineers deal in many different units of pressure including:
Barometers
Meteorologists measure pressure with the aid of a barometer. There are many different types of barometers, the most common being the aneroid and the mercury.
Return to Met 1010-03 Lectures