Measuring Energy Changes
Introduction
Let’s begin our discussion of energy changes by considering the energy changes associated with phase changes, such as melting and freezing or boiling and condensation. These physical processes do not involve any compositional change in the material; it is the same material but in a different physical form. We’ll use the phase changes of water as an example. We are used to seeing water in the solid form as ice, in the liquid form as water, and in the gas form as steam. In order to understand the energy change involved as ice melts, we must first consider how ice and water differ at the molecular level. Both ice and water are composed of the same polar water molecules that form intermolecular hydrogen bonds with each other. One big difference between ice and water is that the individual water molecules in liquid water can flow past each other, meaning that individual hydrogen bonds must be easily broken and reformed such that the individual water molecules move independently of each other. This is not the case in ice, where the individual water molecules are locked in place in a structure that allows for the maximum number of hydrogen bonds.
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The Change in Energy or \(\Delta E\)
We will designate the measured change in energy \(\Delta E\), where \(\Delta\) indicates a change and \(E\) stands for energy. With these conditions in place, any change in energy can be consistently measured as energy is transferred from the system to the surroundings, or vice versa, from the surroundings to the system. This also sets up the energy accounting rule that energy lost or subtracted from the system carries a negative sign, or in accounting terms, an energy withdrawal or debit, and energy gained or added to the system carries a positive sign, or again, in accounting terms, an energy deposit or credit. Finally, for these accounting rules to be valid, no material can be transferred between the system and the surroundings. Energy is the only thing that can be exchanged between the system and the surroundings.
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The Energy Changes of the System or \(\Delta E\)
Energy may be transferred between the system and the surroundings in two ways. We have discussed how heat energy changes are associated with both phase changes and chemical reactions, but energy can also be transferred through work done by the system or on the system. We can state this mathematically as \(\Delta E = q + w\), where \(\Delta E\) is the energy change of the system, \(q\) is the amount of heat energy transferred, and \(w\) is the amount of work done.
If the temperature is held constant, which is one of the rules we set, the work done is pressure–volume work. To better understand what is meant by pressure–volume work, visualize the material of the system in the gas phase and confined in a container with walls that can expand and contract. If the pressure of the gas increases, the force on the container walls increases, and the gas does work on the walls of the container as the walls are pushed outward. Or, if the volume of the container increases, the force on the walls of the container decreases, and the surroundings do work on the gas in the container as the walls move inward. In both cases, work is done.
Pressure–volume work can be stated mathematically as \(w = -\Delta(PV)\), which expands to \(-P \Delta V - V \Delta P\). The negative sign ensures that the work, \(w\), has the correct sign relative to the system.
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The First Law of Thermodynamics
Any energy lost from the system is transferred to the surroundings. It has no other place to go. The converse is also true; any energy lost from the surroundings is gained by the system. Since the signs associated with energy transfer are always set relative to the system, any energy gained by the system must come from the surroundings, or in other words, the amount of energy lost from the surroundings equals the amount of energy gained by the system.
This means the \(\Delta E\) for the surroundings or \(\Delta E_{\text{surroundings}}\) will be equal to but have a sign opposite to \(\Delta E_{\text{system}}\), indicating that it represents energy lost. Mathematically, this can be stated as: \(\Delta E = -\Delta E_{\text{surroundings}}\)
Since the universe represents everything, a change in energy of the universe or \(\Delta E_{\text{universe}}\) would be equal to the change in energy of the surroundings plus the change in energy of the system, or stated mathematically: \(\Delta E_{\text{universe}} = \Delta E_{\text{surroundings}} + \Delta E\)
If we make the substitution \(\Delta E = -\Delta E_{\text{surroundings}}\) in this equation, we get: \(\Delta E_{\text{universe}} = \Delta E_{\text{surroundings}} - \Delta E_{\text{surroundings}} = 0\)
This means that although energy can be transferred between the system and the surroundings, there is no net change in the energy of the universe when energy is transferred between the system and the surroundings. In other words, energy is conserved.
This is the first law of thermodynamics – thermo referring to heat energy and dynamic referring to the movement or transfer of heat energy.
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