The First Law of Thermodynamics

I need to take a tangent from my series on the second law of thermodynamics and discuss the first law of thermodynamics. 

Heat is not a conserved quantity.  Work is not a conserved quantity, but the sum of heat and work is a conserved quantity. The first law is related to the law of conservation of energy; in fact it is one case of that law.

Heat

Heat is a form of energy, often represented by the variable q.  Heat, however is not a state function.  Its value is dependent on the path taken. It is possible to convert heat into work, and it is also possible to convert heat into work work into heat. At some point I need to write a post describing the relationship between heat and temperature, but for now, understand that they are not the same thing.

Work

Work is also a form of energy.  It is often represented by the variable w.  Work can be defined as the integral of force over distance.  Note that force has units of Newtons, distance has units of meters, and that the product is a Joule, a unit of energy.

One type of work that is often of interest in thermodynamics is called PV-work.  PV-work is the integral of pressure over volume.  It is negative because the convention is that work done on a system is positive.  Sometimes engineers use the opposite convention.

Note that pressure has units of Pascals (Pa).  A Pascal is equal to one Newton per meter squared. Volume has units of meters cubed.  Pressure times volume has units of Newtons times meters, otherwise known as Joules.

Work is not a conserved quantity.  It is not a state function.  Its value is dependent on the path taken.  Work can be converted into heat, and heat can be converted into work.

Internal Energy

The sum of heat and work is called the internal energy.  The internal energy is often represented by the variable U; sometimes it is also represented by the variable E.

          ΔU = w + q

The internal energy is a state function.  It is a conserved quantity.  It can neither be created nor destroyed.  The internal energy is independent of the path taken.

Work can be converted to heat, and heat can be converted to work, but the sum of heat and work is a conserved quantity.  This statement is the first law of thermodynamics. In shorthand the first law is sometimes stated as "You can't win."

For a continuing cyclic process, you cannot get more energy out than you put in.

Conservation of Energy

The first law of thermodynamics is a special case of the law of conservation of energy.  Conservation of energy itself is a consequence of Noether's theorem. As long as a physical system is symmetric with respect to  time, energy must be conserved.

Noether's theorem itself is more general, and the various conservation laws can be derived from Noether's theorem.

More on Internal Energy

If the only work done, PV work, then:

     ΔU = q - PΔV

Notice that under conditions of constant volume:

     ΔU = q

Sources

• Atkins, P. W. Physical Chemistry, W. H. Freeman and Company, New York, 3rd edition, 1986
• McQuarrie, Donald A., Statistical Thermodynamics,  University Science Books, Mill Valley, CA, 1973 
• Bromberg, J. Philip, Physical Chemistry, Allan and Bacon, Inc., Boston, 2nd Edition, 1984
• UC Davis Chemwiki: http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/State_Functions
• Wikipedia: Noether's theorem.