Theory — Energy Transfer in Reversible vs Irreversible Processes
Thermodynamic quantities like work and heat depend on the process path.
This calculator compares a quasistatic (reversible) isothermal expansion/compression with an irreversible realization
such as free expansion or constant external pressure.
1) Quasistatic vs non-quasistatic
- Quasistatic (reversible): the system passes through a sequence of equilibrium states, so variables like \(P\) and \(T\) are well-defined at each step.
- Non-quasistatic (irreversible): the system may be far from equilibrium during the change (e.g., free expansion). A single well-defined \(P(V)\) path may not exist for the system.
Even if endpoints are the same, irreversible paths generally produce less useful work than reversible ones.
2) First law and sign conventions
Using the common “work by the system” convention:
Some texts instead use \(W_{\text{on}}=-W_{\text{by}}\), giving \(\Delta U = Q + W_{\text{on}}\).
The calculator lets you choose either convention for reporting \(W\).
3) Isothermal ideal gas: \(\Delta U=0\)
For an ideal gas, internal energy depends only on temperature. If \(\Delta T=0\),
So the first law reduces to \(Q=W_{\text{by}}\) (with the “by-system” convention).
4) Reversible isothermal work
Along a reversible isothermal path, the gas pressure is \(P(V)=\dfrac{nRT}{V}\), so the work is
This is often described as the maximum by-system work magnitude achievable for those endpoints when the process can be made reversible.
5) Irreversible models (path dependence)
A common simple irreversible model is expansion against a constant external pressure \(P_{\text{ext}}\):
Free expansion into a vacuum corresponds to \(P_{\text{ext}}=0\Rightarrow W=0\). If the system is also thermally isolated during free expansion, then \(Q=0\),
and for an ideal gas \(\Delta U=0\) so the temperature remains unchanged.
The key lesson: \(W\) and \(Q\) depend on how the change happens, even when \(\Delta U\) depends only on the endpoints for an ideal gas.
6) Irreversibility and “lost work”
For the same endpoints, the reversible isothermal path provides a benchmark. The difference
quantifies how much by-system work is not obtained because the process is irreversible (in this simplified comparison).
