- The First Law of Thermodynamics states that energy is conserved in an isolated system: energy cannot be created nor destroyed, only transferred.
- Energy (E or U) is transferred as heat (q) or work (w) so any change in energy is given by ΔE=q+w or equivalently ΔU=q+w.
- The heat/work for the system and surroundings have the same magnitudes but opposite signs.
The first law of thermodynamics states that energy is conserved in an isolated system. In the universe, energy cannot be created nor destroyed, but it can be tracked as it moves between the system and surroundings.
Let’s introduce another state function that corresponds to the total energy within a system and call it the internal energy, U or E. The internal energy of a thermodynamic system includes all of the energy (kinetic and potential) within a system, including translational energy, rotational energy, vibrational energy, intermolecular interactions, and electronic energies.
For a monoatomic ideal gas, the internal energy of the system relates directly to its temperature (i.e., average kinetic energy) because potential energies are eliminated. This relationship is given by
where n is the number of moles of gas, R is the gas constant, and T is the temperature.
It is difficult to directly measure the internal energy of non-ideal gas systems in a particular state because we must also consider potential energies. Instead, it is easier to measure how the internal energy changes as a system changes states. This is mathematically described as ΔE or ΔU, where:
If energy is restricted to move only as heat, q, or work, w, then the change in energy must be given as:
For the remainder of the text in this book, we will use ΔU to represent the change in internal energy. Anywhere you see ΔU, you could equivalently use ΔE.
Avoid this common error
It is an error to write Δq or Δw because that implies Δq = qf - qi (or Δw = wf - wi), which does not make sense as the initial and final states of a system do not have heat or work. Heat and work are energy fluxes that change the state of the system during a process (i.e. they are process variables). Only changes in state variables (which are path-independent) are written as ΔX. Process variables are path dependent, and cannot be written as Δq or Δw.
The signs of heat and work for the system are defined such that any change that contributes to an increase in the energy of the system is positive. When heat is absorbed by the system from the surroundings, it is positive for the system (and negative for the surroundings). When heat leaves the system and enters the surroundings, it is negative for the system (and positive for the surroundings).
When work is done on the system, the direction of energy transfer is into the system, so work is positive for the system (and negative for the surroundings).
When work is done by the system, the energy transfer is out of the system to the surroundings. In this case, work is negative for the system (and positive for the surroundings).
We can apply the first law to the system or the surroundings:
The universe is the entirety of the system and surroundings, so the total change in internal energy for the universe is the sum of the changes in the system and surroundings:
Using the above equation we can conclude that
That is, as a consequence of the conservation of energy, the magnitude (amount) of energy that is transferred is the same for both the system and surroundings.
Note that there can be no quniv or wuniv, as there is nowhere outside the universe for the energy to come from or go to. The universe is an isolated system (no energy or matter can cross the boundary and be “outside” the universe), and ΔU for any isolated system is zero.
Interactive: