Is energy a state function?

Well, have you ever written a function of the energy #E# that defines how it changes based on position, time, etc? (Nope!)

Besides calculating the energy of a photon perhaps, all you have done is written

#DeltaE = [...]#

i.e. you only care about the change in energy, because it is a state function.

Examples of equations that involve changes in energy are:

#DeltaE = -2.18 xx 10^(-18) "J" cdot (1/n_f^2 - 1/n_i^2)#
The Rydberg equation for the hydrogen atom.

#DeltaE = q + w#
The first law of thermodynamics, where #DeltaE# is the change in the internal energy.

#DeltaH = DeltaE + PDeltaV#
The definition of the change in enthalpy, #DeltaH#, at constant pressure as it relates to the change in internal energy, #DeltaE#, and pressure-volume work #PDeltaV#.

A state function #Y# can always be defined as

#DeltaY = Y_f - Y_i#

for some initial value #Y_i# and final value #Y_f#. No matter what path the energy takes when it changes, it is still not going to matter.

Some common state functions are:

• Energy
• Temperature
• Volume
• Pressure
• Moles
• Mass
• etc.

On the other hand, consider the first law of thermodynamics for a stationary, non-interacting closed system,

#DeltaE = q + w#,

where #q# is heat flow and #w# is work.

(In this case, #E# is the internal energy, but since the system is sitting still and not interacting with other things, #E# here is also the total energy.)

Here, #q# and #w# are both path functions, and by definition, DO depend on the path. In other words, if you do not take the exact path, you cannot replicate the amount of heat, or work, involved.