Understanding Thermodynamics Through the Concepts of Absolute Zero and the Distribution of Molecular Speeds
Thermodynamics is the study of work, heat, and the energy of a system (NASA, 2010). To help explain in more detail the properties of thermodynamics are the laws of thermodynamics. The first law explains that a system’s internal energy can be increased by adding energy to the system or by doing work on the system (Serway & Vuille, 2012). An internal energy system is the sum of both its kinetic and potential energies. The first law more simply states that the change in internal energy of a system is caused by an exchange of energy across the system, typically in the form of heat, or by doing work on the system. This relationship can be represented by the equation:
ΔU = Q + W
ΔU is the change in internal energy, Q is the energy exchanged (heat), and W is the work done on the system.
Often, energy is exchanged with a gas while work is either done on the gas or by the gas. When work is done on the gas, work is negative; whereas, when work is done by the gas, work is positive (Serway & Vuille, 2012). The internal energy of an ideal gas is represented by the expression:
U = (3/2)nRT
For a monatomic gas where its particles consist of only single atoms, its change in internal energy is represented by the equation:
ΔU = (3/2)nRΔT
n is the number of moles, R is the gas constant (8.31 J/Kmol), and ΔT is the change in temperature measured in Kelvins.
Temperature is measured using many different units throughout the world. Americans in the U.S. typically measure temperature in degrees Fahrenheit. More commonly used throughout the world is degrees in Celsius. In physics, Celsius is also commonly used, along with Kelvin. The relationship between Celsius, t, and Kelvin, T, is represented by the expression:
T = t + 273.16
In any ideal gas law equations, temperature should be in units of Kelvin. The Kelvin scale is an absolute scale, meaning that the lower limit of temperature assigned is zero (Department of Physics, 2010). In relation to the Kelvin scale, the expression for the ideal gas law is PV = nRT. When using the ideal gas law, if the number of moles, n, and the volume, v, is held constant, then “absolute zero” corresponds to zero pressure. Absolute zero is the basis for the Kelvin scale, in that -273.16 °C is its zero point, which corresponds as 0 K (Serway & Vuille, 2012).
Although the concept of absolute zero seems to correlate only with temperature, one must consider what temperature actually is. As mentioned above, when energy is exchanged, it is usually in the form of heat. Therefore, temperature could be considered as the average kinetic energy of molecular motion. While considering this relationship, it has been defined that at absolute zero, molecular motion stops. However, this defies Quantum Mechanics, which states that some molecular motion always exists. If temperature were to actually be absolute zero, there would be no temperature to drive kinetic energy. Additionally, Quantum Mechanics explains that although absolute zero would not drive kinetic energy, molecular motion still has potential energy (Department of Physics, 2010). Thus, the molecules would continue to oscillate as the atoms in the molecules stretch and contract.
Now that we know molecular motion never completely stops, we can discuss how molecular motion is related to both temperature and energy. To simply state this relationship, the temperature of a gas is a direct measure of the kinetic energy of molecules moving in a gas (Serway & Vuille, 2012). Therefore, as the temperature of a gas increases, the molecular motion will also increase and have a greater kinetic energy. To represent the wide-range distribution of molecular motion, the expression is used:
f(v) dv = dN
This is the Maxwellian distribution function, where f(v) specifies the number of molecules, dN, having speeds from range v to v + dv (Department of Physics, 2010). The Maxwellian distribution function can be used in many ways, including finding the mean kinetic energy per molecule for an ideal gas. To find , one can add all the kinetic energies of the molecules, and then divide that sum by the total number of molecules. More simply, another way to calculate this is = (3/2)kT (Department of Physics, 2010). The reason one might want to find the number of molecules with a range of speed or the average kinetic energy of one molecule is to better understand how two different molecules can have the same kinetic energy while moving at different speeds. A large molecule will have slow speed compared to a smaller molecule, which will have a much faster speed to have the same molecular kinetic energies. In relation to temperature, a molecule with a lower temperature will experience fewer collisions between molecules while moving. A molecule with a higher temperature will experience more collisions with other moving molecules due to its faster speed.
Now that we understand how work, heat, and energy impact a system in physics, we need to consider why this is important to appreciate as a human. As animals (or humans) do work and create energy, they give off heat. Therefore, thermodynamics can be applied to animal bodies (Serway & Vuille, 2012). As a body’s internal energy changes due to different amounts of energy being lost, this rate of change can also be measured with an equation just as before in the physics world. ΔU = Q + W can still be used, but each value will be divided by the change in time, Δt. As energy flows out of the body as it does work, internal energy and body temperature are kept constant because animals are open systems (Serway & Vuille, 2012). In ordinary physics situations, doing work causes the internal energy and temperature to actually decrease. This is just one way thermodynamics relates to our everyday lives as humans. Thermodynamics is also incorporated into the technology of our world, including how energy is taken from a refrigerator and delivered as heat to the kitchen; how a heat engine takes in energy by form of heat and uses that energy to create new mechanical and electrical energy; or how an air conditioner uses a heat pump to extract energy from the cold outside air and delivers energy in the form of heat to the warmer inside air. By understanding how thermodynamics is a study of physics, it will make it easier to recognize its influence on our everyday lives as well.
1. Department of Physics. (2010). Physics 174/184 lab manual. Oxford: Kendall Hunt.
2. NASA. (2010). What is thermodynamics?. Retrieved from http://www.grc.nasa.gov/WWW/k-12/airplane/thermo.html
3. Serway, R. A., & Vuille, C. (2012). College physics. (9th ed.). Boston: Cengage Learning.