AcademyFirst-Law Thermodynamics
Academy
Thermodynamic Systems
Level 1 - Physics topic page in First-Law Thermodynamics.
Principle
A thermodynamic system is the chosen matter or region whose energy transfers are tracked.
Notation
\(p\)
pressure
\(\mathrm{Pa}\)
\(V\)
volume
\(\mathrm{m^{3}}\)
\(T\)
absolute temperature
\(\mathrm{K}\)
\(n\)
amount of gas
\(\mathrm{mol}\)
\(Q\)
heat transferred to the system
\(\mathrm{J}\)
\(W\)
work done by the system
\(\mathrm{J}\)
Method
Derivation 1: Choose the boundary
Energy accounting starts by deciding what is inside the system. Everything outside is the surroundings, and transfers cross the boundary.
Energy crossing
\[\text{system}\ \longleftrightarrow\ \text{surroundings}\]
Heat sign
\[Q>0\quad\text{when energy enters by heating}\]
Work sign
\[W>0\quad\text{when the system does work on surroundings}\]
Derivation 2: Describe a state
A thermodynamic state is specified by macroscopic variables after the system has settled enough for those variables to be meaningful.
State variables
\[(p,V,T,n)\]
Ideal-gas state
\[pV=nRT\]
This is a model relation for dilute gases in equilibrium.
Process
\[\text{process}=\text{path through states}\]
Rules
These are the system choices used throughout the First Law section.
Ideal gas state
\[pV=nRT\]
Heat sign
\[Q>0\quad\text{into the system}\]
Work sign
\[W>0\quad\text{done by the system}\]
Examples
Question
A gas in a cylinder is compressed by an external piston while heat leaves through the cylinder wall. Identify the signs of \(Q\) and \(W\) for the gas as system.
Answer
Heat leaves the gas, so
\[Q<0\]
Compression means the surroundings do work on the gas, so work done by the gas is negative: \[W<0\]
Checks
- Always name the system before assigning signs.
- Heat and work are transfers across the boundary, not stored properties.
- State variables describe equilibrium states, not arbitrary nonequilibrium details.
- The ideal-gas equation uses absolute temperature.