Real gas
- Particles have volume
- Energy is lost in collisions
- Intermolecular forces
Ideal gas
- Particles have no volume
- Collisions are elastic
- No interactions between particles
Real gases behave like ideal gases at 🔥 High temperatures or 🪣 Low pressures
$$ \underbrace{P}{\text{Pressure in Pa}}\times\overbrace{V}^{\text{Volume in m}^3}=\underbrace{n}{\text{nb. of molecules in mol}}\times \overbrace{R}^{\text{Constant }8.31\,\text{s.i.} }\times \underbrace{T}_\text{Temperature in K} $$
<aside> <img src="https://em-content.zobj.net/source/microsoft-teams/337/moai_1f5ff.png" alt="https://em-content.zobj.net/source/microsoft-teams/337/moai_1f5ff.png" width="40px" /> Intensive variables: are non additive their value is not proportional to the amount of substance
Extensive variables: are additive their value is linearly proportional to the amount of substance
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$$ \underbrace{\Delta E}\text{Change in internal energy}=\underbrace{W}\text{Work done on system}+\underbrace{Q}_\text{Heat supplied to system} $$
$$ \newcommand{\dbar}{\text{d}\hspace*{-0.16em}\bar{}\hspace*{0.2em}} \text{d}E=\dbar Q+\dbar W $$
For a process to be reversible:
- it must be quasistatic (proceeds very slowly, such that the system is always instantaneously in thermal equilibrium)
- there must be no external friction
- it must not cause any permanent change to the system (e.g. stretching a wire beyond its elastic limit)
$$ \text{d}\hspace*{-0.16em}\bar{}\hspace*{0.2em}W=\vec F \cdot \text d \vec x=\underbrace{\frac{|\vec F|}{A}}{P}\underbrace{A \, \text dx}{-\text dV}=-Pd\text V $$
Example: The tension $\Gamma$ in an elastic string stretched to a length $L$ at a temperature $T$ is
$$ \Gamma=KT\left(\frac{L}{L_0}-\frac{L_0^2}{L^2}\right) $$
Calculate the work done on the string when it is stretched reversibly and isothermally.
