# Physical Chemistry/Introduction to Thermodynamics

Thermodynamics is a misnomer since we will only consider equilibrium phenomena, not time-dependence like in kinetics. Thermodynamics deals with things like energy, entropy, volume, heat, work, efficiency. (ideal), free energy, chemical potential, pressure, temperature. It was developed to explain steam engines back in the 1800's. It has come a long way since then, able to explain a vast array of phenomena in chemistry, physics, and biology. It is an old theory, but a beautiful one. It is very important in chemistry.

Sample problem

An ideal monoatomic gas at 1 bar is expanded in a reversible adiabatic process to a final pressure of ${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$ bar. Calculate ${\displaystyle q\;}$ per mole, ${\displaystyle w\;}$ per mole, and ${\displaystyle \Delta {\overline {U}}}$.

To solve this, we need to apply the fact that ${\displaystyle {\frac {T_{2}}{T_{1}}}=\left({\frac {P_{2}}{P_{1}}}\right)^{\gamma -1/\gamma }}$.

So, substitute and solve for ${\displaystyle T_{2}}$

${\displaystyle {\frac {T_{2}}{298.15\ K}}=\left({\frac {0.5\ bar}{1.0\ bar}}\right)^{\begin{matrix}{\frac {{\begin{matrix}{\frac {5}{3}}\end{matrix}}-1}{\begin{matrix}{\frac {5}{3}}\end{matrix}}}\end{matrix}}}$

${\displaystyle T_{2}={225.96\ K}}$

Now, we use

${\displaystyle w=\int _{T_{1}}^{T_{2}}{\overline {C}}_{v}\,dT}$

Which will give us ${\displaystyle w}$

${\displaystyle w=\int _{298.15\ K}^{225.96\ K}{\overline {C}}_{v}\,dT={\begin{matrix}{\frac {3}{2}}\end{matrix}}R\left(225.96\ K-298.15\ K\right)=-900.39\ J\ mol^{-1}}$

Hence, we have all of our answers...

Adiabatic means ${\displaystyle \Delta {\overline {U}}=w}$, so ${\displaystyle q=0\ J\ mol^{-1}}$ and ${\displaystyle w=-900.39\ J\ mol^{-1}}$ while ${\displaystyle \Delta {\overline {U}}=-900.30\ J\ mol^{-1}}$

## The Zeroth Law of Thermodynamics

This law of thermodynamics was developed after the establishment of the first and second laws of thermodynamics. The zeroth law is involved in defining temperature.

Let us consider three systems, A, B, and C. If systems A and C are in equilibrium, and B and C are in equilibrium, then A and B will be found to be in thermal equilibrium when connected by a heat conductor. This associative property of systems is the zeroth law of thermodynamics.

The zeroth law of thermodynamics states that if two systems are in thermodynamic equilibrium seperately with a third system then both these systems are said to be in thermodynamic equilibrium with each other.