Physics 5B overview
Universal behaviors
This course covers a wide range of topics: thermodynamics, fluids, oscillations, waves, and optics. While this might appear to be a random collection of topics, there is a unifying theme here. All of these topics describe universal behaviors of physical systems: behaviors that appear in the same form in many different systems throughout nature.
Often, these universal behaviors appear in superficially different forms while still obeying the same underlying laws:
- A mass on a spring, a swinging pendulum, and a vibrating molecule can all undergo the same patterns of oscillation.
- Sound, water waves, and light all exhibit interference and diffraction.
- Energy and entropy constrain all macroscopic systems, ranging from relatively simple systems like gases to complex living organisms.
Exploring the physics of matter
Another unifying theme in 5B is that we explore physics beyond the simple mechanical models (e.g., point particles) you saw in Physics 5A. In particular, we will focus largely on macroscopic systems consisting of very many particles, and we will often model these systems as continuous media rather than collections of points.
This broader perspective will allow us to study how matter stores and transports energy, how information and energy propagate through materials, and how light interacts with matter. If Physics 5A left you thinking that physics is mostly about blocks sliding on inclines, Physics 5B will broaden that picture and bring us much closer to understanding the behavior of real physical systems, especially biological systems and the human body.
Thermodynamics and energy
From motion to matter
In mechanics, we learn how to model objects in motion, without much concern for the internal structure or properties of these objects. For example, you may have discussed how thermal energy is generated by friction when an object slides on a surface, but not how the temperature of the object changes as a result of this friction.
In Physics 5B, we will cover how material properties of systems change in physical processes and how macroscopic properties are connected to the behavior of the atoms and molecules that make up matter.
Thermodynamics studies macroscopic properties
As you know, matter consists of an enormous number of microscopic particles. For example, a cup of water contains on the order of $10^{25}$ $\mathrm{H_2O}$ molecules. Because the number of particles is so large, it’s practically impossible to study macroscopic systems by modeling the motion on the level of individual particles.
One way to get around this problem is to simply ignore it! (This is typically not a good way to deal with your problems, but sometimes we can get away with it in physics. Arguably, this is the reason many people decide to study physics.) That is, we can “zoom out” and study from a macroscopic view, without worrying about what is happening on the level of individual particles. This means focusing on a small number of measurements that we can make on a system as a whole, and how these measurements change in physical processes. We call this approach thermodynamics.
For example, some of the macroscopic properties we can measure are pressure $p$, temperature $T$, mass $m$, and volume $V$.
Energy to the rescue
Given that we can’t model the motion of individual particles in a macroscopic system using Newton’s laws, what tools do we have available to study such systems? Fortunately, there is one physical principle that applies to all systems regardless of the microscopic details: the law of conservation of energy.
Recall the statement of this law from Physics 5A: energy cannot be created or destroyed. For any choice of system, the total energy change of the system and environment must be zero:
\[\Delta E_{\mathrm{sys}} + \Delta E_{\mathrm{env}} = 0\]The energy principle
Another way to express energy conservation without explicitly referring to the environment is called the energy principle. It says that the total change in the energy of a system is equal to the net flow of energy into the system:
\[\Delta E_{\mathrm{sys}} = \text{net energy flow into the system}\]In thermodynamics, we are only interested in the energy associated with the microscopic particles inside a system. We call this microscopic energy the internal energy $E_{\mathrm{int}}$.
When we apply the energy principle to a thermodynamic system to relate the change in internal energy to the net energy flow into the system, we refer to it as the first law of thermodynamics.
Temperature
Temperature as a proxy for internal energy
In general, there is no way to measure the internal energy of a system directly. If we want to know how the internal energy of a system changes, we need a measurable, macroscopic property that is related to the internal energy. This property is the temperature $T$ of the system.
It is important to emphasize that temperature is not the same as internal energy. However, if the temperature of a system changes (with no other changes to the system) then the internal energy of the system will change. In this sense, temperature is a useful proxy for internal energy.
In later chapters, we will see how the internal energy and temperature are connected. For now, just keep in mind that increasing the temperature of a system also increases its internal energy.
Defining temperature
From everyday life, you are familiar with temperature as a measure of how hot or cold something is. This is the right intuition for what temperature measures, but we can make this more precise.
Let’s start by thinking about what “hot” and “cold” actually mean. In particular, these are relative terms: a system is only hot or cold compared to some other system. For example, if you leave a glass of ice water at room temperature, the ice will melt and the water will heat up until it reaches room temperature. On the other hand, a hot cup of coffee left at room temperature will cool down until it reaches room temperature. The air in the room is hot compared to the ice water, but cold compared to the coffee.
Thermal equilibrium
When two systems at different temperatures are in contact, energy will spontaneously flow from the hotter system to the colder system. If the two systems are left in contact for long enough, they will eventually reach the same temperature. When this happens, we say that the two systems are in thermal equilibrium.
We can take this as the defining property of temperature:
The temperature of a system measures its tendency to spontaneously give up energy to other systems. Two systems have the same temperature when they are in thermal equilibrium.
Temperature scales
In the SI system, there are two different notions of temperature: the Celsius temperature, measured in degrees Celsius ($^\circ\mathrm{C}$), and the thermodynamic or absolute temperature, measured in kelvins ($\mathrm{K}$). Both are used frequently.
In contrast with the Celsius scale, the Kelvin scale is an absolute scale, which means that a temperature of $0\ \mathrm{K}$ is the lowest possible temperature (“absolute zero”). Thinking of temperature as the tendency to spontaneously give up energy, this means that a system at $0\ \mathrm{K}$ can never spontaneously give up energy to its environment.
One advantage of the Kelvin scale is that ratios of absolute temperatures are physically meaningful, so many formulas we will see (like the ideal gas law) require temperatures in kelvins. Ratios of Celsius temperatures have no physical meaning.
Historically, the Celsius scale is based on the boiling and freezing temperature of water. Water freezes at $0^\circ\mathrm{C}$ and boils at $100^\circ\mathrm{C}$. In the modern SI system, the kelvin is defined first, and the Celsius temperature is defined in terms of the absolute temperature. Writing $T[\mathrm{K}]$ for the numerical value of the absolute temperature and $T[^\circ\mathrm{C}]$ for the numerical value of the Celsius temperature, the two are related by
\[\boxed{T[^\circ\mathrm{C}] = T[\mathrm{K}] - 273}\]Note that temperature differences are the same in both scales,
\[\Delta T[^\circ\mathrm{C}] = \Delta T[\mathrm{K}],\]so we can use them interchangeably for temperature differences.
Heat and the first law of thermodynamics
Heat
The energy principle relates the change in energy of a system to the flows of energy into or out of the system. The relevant change in energy in thermodynamics is the change in internal energy, $\Delta E_{\mathrm{int}}$. What are the energy flows we need to consider?
In Physics 5A, you considered only one type of energy flow: the work done by macroscopic forces on objects. In the preceding discussion on temperature, we saw another type of energy flow: the spontaneous flow of energy due to a temperature difference. This energy flow is commonly called heat and denoted by the symbol $Q$:
\[\boxed{Q = \text{energy flow due to temperature difference}}\]Caution: Heat is not a property of a system. It is a transfer of energy between a system and its environment.
Energy flows in thermodynamics
In thermodynamics, any energy flow that is not due to a temperature difference is considered work. The net work done on a system by its environment is denoted $W$.
Note that the quantities $Q$ and $W$ represent the flow of energy into a system from the environment. Positive values of $Q$ and $W$ indicate energy transfer into the system, while negative values indicate energy transfer out of the system.
Writing out the thermodynamic energy principle explicitly, we have
\[\boxed{\Delta E_{\mathrm{int}} = Q + W}\]As mentioned earlier, this form of the energy principle is called the first law of thermodynamics.