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1st law

Conservation of energy: The first law of thermodynamics

In the introduction, several examples were presented of systems we can consider from our chemical thermodynamic perspective. What types of energy do such systems possess? What can be said regarding processes occurring in these systems that involve changes in their internal energy? The first law of thermodynamics, which we put on a firm basis in this section, is an important statement that applies to any process.
 

For any process, the change in internal energy U(n, T, P,V) is in general expressible as the final value of U minus its value before the process has occurred. This energy change is written as ΔU. Because the actual value of U is quite large, it is only practical to measure ΔU. There are two quantities, heat and work (described further below) that - when measured for a process involving no matter exchange - determine ΔU for the process. The results of such measurements have demonstrated that any gain or loss of energy ΔU(sys) is exactly compensated for by loss or gain of energy by the surroundings, ΔU(surr). In other words, energy is neither created nor destroyed in any process, and is thus always conserved. This is a clear statement of the first law of thermodynamics.

The equation ΔU(total) = ΔU(sys) + ΔU(surr) = 0 is of course the mathematical formulation of this statement. The first law of thermodynamics has been established by many careful measurements of the heat and work associated with various processes. Let us consider the nature of heat and work.

Heat can be decsribed as a form of energy that is transferred between system and surroundings as a result of a temperature difference between them. The conventional symbol for this form of energy is q.

Work (in general symbolized as w) can be divided into different types. Most commonly, we consider mechanical and electrical work. The definition of mechanical work from physics - in its simplest form - is that work is a quantity corresponding to a constant force F acting through a distance d. We will consider mechanical work in the form of pressure-volume work (P-V work). If a gas in a closed system with a movable boundary - such as a balloon or a piston within a cylinder - expands against an external pressure Pext, work has been performed by the system, and the amount of work is given by the relation w = –Pext(ΔV). The system is said to have done work on the surroundings, and in this case, the sign of w is negative, since this will correspond to a loss of energy from the system. You should verify that both the products P·V and F·d give rise to units of energy.

We will see from examples of processes that both the amount of heat transferred q and the work w done will depend on the particular path a process follows intaking the system from an initial state to a final state. Imagine a closed system in which a process occurs, accompanied by a change in volume of the system. In this case, the system may do work on the surroundings or vice-versa. In the former case, the system gives up energy to do the work on the system, while in the latter case, the system acquires energy by virtue of the surroundings doing work on it.

Energy changes and examples of energy conservation
The equation ΔU(sys) = q + w can be taken as a statement of the first law of themodynamics under the conditions we have specified, since under these conditions we have accounted for all energy inputs and outputs from the point of view of the system, with the constraint that total energy of the universe remains constant satisfied. In some discussions of the first law, one will see the equation written as ΔU(sys) = q – w, in which work done by the system on the surroundings is given a postive sign. This is the first law from an engineer's point of view, since engines are systems capable of performing useful work (on the surroundings) given an energy input. A heat engine - the classic example being a steam engine - can take energy in the form of heat and produce mechanical work, such as the rotation of a driveshaft. We will use the convention that work done by the system on the surroundings is negative in sign, since this keeps our attention focused on the energy balance sheet of the system of interest. Heat transferred to or work done on the system (q or w positive) increases its internal energy. If the system gives up heat to the surroundings (q negative), or performs work on the surroundings (w negative), its internal energy must correspondingly decrease.
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