# What is thermodynamics?

Jan 29, 2016

Thermodynamics involves processes associated with heat changes, often in relation to energy and work, in specific atmospheric conditions.

Whether in chemistry or physics, thermodynamics tends to involve the internal energy $U$, heat flow $q$, and work $w$, each of which jointly constitute the First Law of Thermodynamics.

You may also discuss some form of enthalpy $H$, entropy $S$, and Gibbs' free energy $G$, and perhaps the Helmholtz free energy $A$, which tend to describe heat flow in various conditions, like constant temperature, pressure, or volume.

Some equations that generally sum up some of the most prevalent concepts in thermodynamics:

FIRST LAW OF THERMODYNAMICS

$\setminus m a t h b f \left(\Delta U = q + w = q - P \Delta V\right)$

where:

• $U$ is the internal energy, a state function. It can be considered the heat flow at constant volume.
• $q$ is the heat flow, a path function.
• $w$ is the work, a path function.

This basically says that the internal energy of a system is determined by the heat flow in/out of the system and the expansion/compression work done upon the system.

SECOND LAW OF THERMODYNAMICS

$\setminus m a t h b f \left(\Delta {S}_{\text{univ" = DeltaS_"sys" + DeltaS_"surr}} > 0\right)$

where $\Delta S$ is the entropy, or the disorder. I think you can tell that "sys" means system and "surr" means surroundings (e.g. outside of the system).

This really says that the entropy of the universe always increases, though entropy of the surroundings or of the system could be negative, as long as $\Delta {S}_{\text{univ}} > 0$.

That's because although the entropy of the universe always increases, it might not for a nonideal system where stuff can leak out.

THIRD LAW OF THERMODYNAMICS

$\setminus m a t h b f \left(\Delta S = {k}_{B} \ln \Omega\right)$

where:

• ${k}_{B}$ is the Boltzmann constant, $1.3806 \times {10}^{- 23} \text{J/K}$
• $\Omega$ is the number of microstates for any given macrostate

For any perfect crystalline solid at $\text{0 K}$, insofar as all of its particles are identical (the number of permutations for the particles is $\Omega = 1$), the entropy change is $0$. Notice that when $\Omega = 1$, $\ln \Omega = 0$.

ENTHALPY VS INTERNAL ENERGY AND PV WORK

$\setminus m a t h b f \left(\Delta H = \Delta U + \Delta \left(P V\right)\right)$

where:

• $H$ is enthalpy, which can be considered the heat flow at constant pressure.
• $U$ is internal energy, which can be considered the heat flow at constant volume. It is equal to $q + w = q - P \Delta V$.
• $P$ and $V$ are pressure and volume, respectively, and $\Delta \left(P V\right) = P \Delta V + V \Delta P + \Delta P \Delta V$ via the "product rule".

From this, for example, you can derive how enthalpy is equivalent to the heat flow $q$ at constant pressure.

Normally, from the above equation you would simplify it down to $\Delta H = q + V \Delta P + \Delta P \Delta V$, so when $\Delta P = 0$, $\Delta H = q = {q}_{p}$.

This is the condition under which you do General Chemistry problems where you immerse a metal in water for instance, or where you are asked to calculate the heat released by a reaction you would find in a standard thermodynamics reference table.

"THE" THERMOCHEMISTRY EQUATION

$\setminus m a t h b f \left(\Delta G = \Delta H - T \Delta S\right)$ at const. $T$

where:

• $G$ is Gibbs' free energy, which can be considered the maximum amount of non-PV work that can be performed as a result of a particular process.
• Other variables are ones you have seen before and mean the same as in the above equations.

You would usually use this to determine spontaneity based on the temperature, entropy, and enthalpy values you have for a particular process.

You could also have a similar relation involving the Helmholtz free energy, which you may or may not talk about for a while.

$\Delta A = \Delta U - T \Delta S$

I'm not going to discuss the Helmholtz free energy, but you can look it up if you want to know more about it.