The First Law of Thermodynamics

In his book, "A Short History of Nearly Everything" (Broadway Books, New York, 2003), Bill Bryson quotes the chemist P.W. Atkins on the Laws of Thermodynamics: "There are four Laws. The third of them, the Second Law, was recognized first; the first, the Zeroth Law, was formulated last; the First Law was second; the Third Law might not even be a law in the same sense as the others."

Confused? Let's take a look at these.  We've already discussed the Zeroth Law of Thermodynamics: If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. A system is simply the object or objects that we want to explore. A closed system is one where no mass may enter or leave the system. Energy, however, may enter and leave the system. An isolated system is a closed system that does not allow energy to enter or leave the system. Finally, an open system is a system where both mass and energy are free to enter or leave the system. The First Law of Thermodynamics is the Law of Conservation of Energy. Simply stated, the change in internal energy (DU) of a closed system is equal to the heat added (Q) to a system minus the work done (W) on a system.Mathematically, we state it as:

DU=Q-W

There is a sign convention associated with this that is important to remember:

  • When Heat is added to a system, Q is Positive.
  • When Heat is removed from a system, Q is negative.
  • When work is done on a system (such as compressing a gas), W is negative.
  • When work is done by a system (such as a gas expanding), W is positive.

We need to keep track of these signs when we do problem solving with the First Law.

There are some processes that take place in a system. Remember, we are going to be exploring the behavior of gases here, and looking at how a system changes in terms of the Internal Energy, Heat, and Work, as well as the effects of pressure, temperature, and volume. In all of these cases, we use Pressure-Volume (or P-V) diagrams to show the process. The clues given in our definitions can help us to remember what the process looks like on a P-V diagram. The work done by a gas is the area under the curve. So let's get some more definitions under our belts:



An isothermal process is one where temperature does not change during the process. pressure and volume may both change, but the temperature will remain constant. If we recall that the change in internal energy of a system is given by the equation

then if there is no change in temperature, there is no change in internal energy. Hold that thought.

An isobaric process is one where the pressure is held constant but the volume and temperature are free to change. In a piston, for example, the work done by the piston is equal to the force on the piston times the distance the piston moves. Since force equals the pressure times the area, this may also be expressed as

 

W = PADd


But Area times distance is volume, so the work done may be expressed in terms of the pressure and the
change in volume of a system, or:

W = PDV

In an isobaric process, we hold the pressure constant so the work is proportional to the change in volume of the system. The diagram at the left shows the work done by a gas in an isobaric process. Recall that we said the work on a P-V diagram is the area under the curve. This illustrates, perhaps, the simplest case of that formula.

An isochoric (or isovolumetric) process is one where the volume is held constant but the pressure and temperature are free to change. Here, we can go back to the formula we just looked at and see that, if the volume of the system does not change (DV = 0), then there is no work done on or by the system. Finally, an adiabatic process is one where no heat is allowed to enter or leave the system. In this case, Q = 0. This only happens in very fast reactions or when a system is very well insulated. The PV diagram for an adiabatic process looks like an isothermal process.

For more information, try the following links:

http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1.html

http://www.physicalgeography.net/fundamentals/6e.html

http://physics.bu.edu/~duffy/py105/Firstlaw.html

For Practice Problems, Try:

First Law Problem

Work to Compress a Gas

Giancoli Multiple Choice Practice Questions (Questions 1-10)