AcademyFirst-Law Thermodynamics
Academy
Internal Energy and the First Law
Level 1 - Physics topic page in First-Law Thermodynamics.
Principle
The first law is energy conservation applied to a thermodynamic system.
Notation
\(U\)
internal energy
\(\mathrm{J}\)
\(\Delta U\)
change in internal energy
\(\mathrm{J}\)
\(Q\)
heat transferred to the system
\(\mathrm{J}\)
\(W\)
work done by the system
\(\mathrm{J}\)
\(W_{\mathrm{on}}\)
work done on the system
\(\mathrm{J}\)
Method
Derivation 1: Account for energy crossing the boundary
Heat added raises the system energy if nothing else happens. Work done by the system lowers the system energy because energy leaves mechanically.
Heat input
\[Q>0\Rightarrow U\ \text{tends to increase}\]
Work output
\[W>0\Rightarrow U\ \text{tends to decrease}\]
First law
\[\Delta U=Q-W\]
Derivation 2: Convert sign conventions
Some problems give work done on the system instead. That is the negative of work done by the system.
Work sign conversion
\[W_{\mathrm{on}}=-W\]
On-system form
\[\Delta U=Q+W_{\mathrm{on}}\]
Adiabatic case
\[Q=0\Rightarrow \Delta U=-W\]
Rules
These are the first-law forms used in this course.
First law
\[\Delta U=Q-W\]
Work on system
\[\Delta U=Q+W_{\mathrm{on}}\]
Adiabatic transfer
\[Q=0\Rightarrow\Delta U=-W\]
Cyclic transfer
\[\Delta U=0\Rightarrow Q=W\]
Examples
Question
A gas absorbs
\[650\,\mathrm{J}\]
of heat and does \[240\,\mathrm{J}\]
of work. Find \[\Delta U\]
Answer
\[\Delta U=Q-W=650-240=410\,\mathrm{J}\]
Checks
- State the work sign convention before substituting numbers.
- \(Q>0\) means heat enters the system.
- \(W>0\) means the system does work on the surroundings.
- Internal energy is a state function; heat and work are not.