The First Law of Thermodynamics
One of the most important observations in science is that energy can be neither created nor destroyed, in other words Energy is conserved. Any energy lost by the system must be gained by the surroundings, and vice versa. This important and fundamental observation is known as the first law of thermodynamics. To apply this law quantitatively, we must first define the energy of a system more precisely. Let us, for example define our system as a mole of hydrogen gas and a mole of oxygen gas confined in a cylinder. The cylinder would be part of the surroundings. The total energy of our system is the sum of all the kinetic and potential energies of its component parts. This would include not only the motions and interactions of the hydrogen and oxygen molecules themselves but also of their component nuclei and electrons. This total energy is called the internal energy of the system. Because there are so many types of motions and interactions, we cannot determine the exact energy of any real system. But we can measure the changes in internal energy that accompany chemical and physical processes.
We define the change in internal energy, which we represent as ΔU, as the difference between the internal energy of the system at the completion of a process and that at the beginning:
ΔU = Ufinal - Uinitial
Thermodynamic quantities such as ΔU, have three parts: a number and a unit giving the magnitude of the change, and a sign giving the direction. A positive ΔU results when Ufinal > Uinitial, indicating that the system has gained energy from its surroundings. A negative ΔU is obtained when Ufinal < Uinitial, indicating that the system has lost energy to its surroundings.
Heat and Work
A system can exchange energy with its surroundings in two general ways: as heat or as work. The internal energy of a system changes in magnitude as heat is added to or removed from the system, or as work is done on it or by it. These ideas are used to write a very useful algebraic expression of the first law of thermodynamics. When a system undergoes any chemical or physical change, the accompanying change in its internal energy, ΔU, is given by the heat added to or removed from the system, q, plus the work done on or by the system, w:
ΔU = q + w
When heat is transferred from the surroundings to the system, q has a positive sign. Likewise when work is done on the system by the surroundings, w has a positive value.
Example
Suppose that during a chemical reaction, a system loses 1100 J of heat to the surroundings, and the system does 500 J of work on the surroundings. What is the change in internal energy of the system?
We are told that the process is exothermic, that is it loses heat so q = -1100 J and since the system did work on the surroundings (it had to use some of its internal energy to do that), w -500 J.
ΔU = q + w = (-1100 J) + (-500 J) = -1600 J
State Functions
Although scientists have no way of knowing the precise value of the internal energy of a system, they do know that it has a fixed value for a given set of conditions. Furthermore, the total internal energy of a system is proportional to the total quantity of matter in the system; energy is an extensive property.
Suppose we define our system as 30 g of water at 25oC and 1 atm. Our system could have arrived at that state in a number of ways, cooling 30 g at 80oC and 1 atm to 25oC and 1 atm or maybe by heating 30 g at 0oC and 1 atm to 25oC and 1 atm. The internal energy of our system, 30 g of water at 25oC and 1 atm is the same no matter how it arrived at this condition. The internal energy of a system is a state function. The value of a state function does not depend on the particular history of the sample, only on its present condition.
Though some thermodynamic quantities are state functions others are not. As an example, we will consider a flashlight battery as our system and let the change in the system be the complete discharge of the battery at constant temperature. If the battery is discharged in a flashlight, no mechanical work is done. All the energy lost from the battery appears as radiant energy and heat. On the other hand, if the battery is used in a toy car, the same change in state of the battery produces mechanical work and heat. The change in state of the system and thus the change in internal energy, ΔU, are the same in both cases. But the amount of work done in the two cases is different, as is the amount of heat released. So we see that although ΔU is always the same for a given change in the system, the way in which the change is carried out will determine the values of q and w, the means by which energy is transferred.
Enthalpy
Most physical and chemical changes, including the very important ones in living systems, take place under the essentially constant pressure of the Earth's atmosphere. For example, laboratory reactions are usually carried out in containers that are open to the atmosphere, such a beakers and test tubes. For most of these processes, especially those that don't involve gases, only small amounts of work are performed as the system expands or contracts slightly against the force of the atmosphere. Thus most of the energy gained or lost by the system during these processes is in the form of heat. Because this energy is so important in chemistry, we define a quantity called enthalpy in dealing with the heat absorbed or released under constant pressure. Enthalpy is denoted with the symbol H. Like internal energy, enthalpy is a state function, also with enthalpy we can only measure changes and not absolute values of enthalpy. The change in enthalpy, ΔH, equals the heat, qp, gained or lost by the system when the process occurs under constant pressure:
ΔH = Hfinal - Hinitial = qp
The subscript P on the heat, q, indicates the special case in which the pressure is constant. Only under this special case of constant pressure is the heat transferred equal to the change in enthalpy. Because ΔH equals a quantity of heat, the sign on ΔH indicates the direction of heat transfer. A positive sign indicates that the system has gained heat from the surroundings, which is an endothermic process. When ΔH is negative, the system has released heat to the surroundings, which is an exothermic process.