Laws of Thermodynamics

The Four Laws

The Zero Law: Chemists originally came up with three laws, and then realized they forgot the most important one, so they called it the Zeroth Law of Thermodynamics, which states that Temperature is a transitive property. Recall from Pre-Algebra (I know, it’s been a while) that the transitive property is: if A = C and B = C, then A = B. Replace the equal sign with “is at thermal equilibrium with” and we get the Zeroth law – if a system can be brought into thermal equilibrium with two other, separate systems, then the two other systems can also be brought into thermal equilibrium with each other. This concept allows us to prove that there is some criteria for thermal equilibrium, paving the way for us to be able to measure temperature. In essence, that is what this law says: that temperature exists and can be measured. Here is a more difficult question though: What is temperature, quantitatively?

For an ideal gas, absolute temperature is proportional to average translational kinetic energy per particle: ⟨KE⟩=3k_BT/2. Kinetic energy depends on speed squared. This ideal-gas relation is not a complete description of the internal energy of every substance in every state.

For a gas of the same composition, both the mean speed and root-mean-square speed vary as √T, with T in kelvin. Speed is a magnitude. The vector average velocity of a gas at rest is zero because particle motions point in different directions.

Example Problem 8.1.1

The First Law: This is probably the most famous law in thermodynamics. It is also called The Law of Conservation of Energy, because it states that energy can neither be created nor destroyed. It simply changes form. In order to fully understand this law, it is important to realize that there are many types of energy. These are covered more in depth in Physics.

Kinetic Energy is the energy of an object due to its movement.

Potential Energy is the energy of an object that can be converted into a different form of energy (sub-types include gravitational potential energy, electrical potential energy).

Chemical Energy is the energy released due to chemical reactions, such as our body using up nutrients.

Electrical Energy is energy due to the movement of electrons.

Heat is energy transferred between a system and its surroundings because their temperatures differ. Thermal energy describes microscopic energy associated with particle motion and interactions; heat is a transfer, rather than energy stored in an object. Thermal energy can participate in work-producing processes subject to thermodynamic limits.

The Second Law: Although the first law is the most well-known, the second law is the most important law to understand. The second law of thermodynamics is not only the most important law in Thermodynamics or Chemistry, many people would argue that it is the most important law in all of the sciences because of its applications and implications.

Entropy is a state function associated with the distribution of energy among accessible microscopic arrangements. More accessible arrangements generally correspond to greater entropy. “Disorder” can be a useful informal image, but visual messiness alone is not a quantitative rule for predicting ΔS.

The second law concerns the total entropy change of a system plus its surroundings. For an isolated total system, ΔS_universe is positive in an irreversible spontaneous change and zero in an ideal reversible change. The system’s own entropy can decrease if its surroundings gain enough entropy.

Gibbs free energy combines enthalpy and entropy: G=H−TS. At constant temperature and pressure, with only pressure–volume work, a spontaneous change decreases the system’s G. For a reaction, ΔG<0 favors the forward direction, ΔG>0 favors the reverse direction, and ΔG=0 at equilibrium.

In ΔG=ΔH−TΔS, use temperature in kelvin and consistent energy units. ΔH and ΔS can each be positive or negative. ΔG applies to the current composition; ΔG° applies to the defined standard states. Thermodynamic favorability does not tell you how fast a reaction occurs.

Enthalpy is the state function H=U+PV. Its change describes the difference between specified initial and final states. At constant pressure, when pressure–volume work is the only work, ΔH equals q_p, the heat transferred into the system. A negative ΔH means the system releases heat to its surroundings.

Example Problem 8.1.2

Reviewed conceptual task: why is a comparison of “enthalpy per mole of gasoline” and carbon dioxide incomplete without a named fuel composition, specified physical states and thermochemical reference?

Over the next few sections, we will strengthen our applications of these concepts in chemical reactions and become comfortable using the various new equations introduced in thermodynamics.

Most of the rest of the chapter focuses on the first and second laws, as these have the greatest quantitative applications, especially in chemistry. Until then, let’s discuss the final law.

Absolute-zero and low-temperature research use careful definitions of temperature and entropy. For AP Chemistry, use the perfect-crystal third-law limit to understand the reference for absolute molar entropies. The third law does not remove the conditions or limits in the second law.