Statistical Physics: Reversible and Irreversible Processes

Study Notes

A system in thermodynamic equilibrium has constant pressure, volume, and temperature over time.
An insulating cylinder with a conductive base can interact thermally with a reservoir at temperature T.
Irreversible Processes:
- Rapid depression of the piston leads to turbulence, with undefined pressure and temperature.
- Cannot plot a continuous line on a PV diagram; transitions through non-equilibrium states.
- It is defined as moving from one equilibrium state to another without retracing the path.
Reversible Processes:
- Slow depression of the piston maintains well-defined pressure, volume, and temperature throughout.
- Can be plotted as a continuous line on a PV diagram, transferring heat Q to the reservoir.
- A differential environmental change allows retracing the path back to the initial state.
Quasi-state processes are those that pass through a continuous sequence of equilibrium states but may not necessarily be reversible.

An adiabatic process does not allow heat transfer into or out of the system.
Can be reversible (slowly moving the piston) or irreversible (rapidly pushing the piston).
In adiabatic compression, the gas’s temperature increases, and internal energy changes differ between reversible and irreversible cases.

Heat engines convert heat into useful work by absorbing energy as heat and expelling some as work.
An example setup involves a gas in a cylinder interacting with a thermal reservoir.
An effective engine returns to its starting point after a cycle to maintain operation continuously.
Sign Conventions:
- Heat entering the system is positive; leaving is negative.
- Work done on the system with volume decrease is positive; work done by the system with volume increase is negative.
A cyclic process is characterized by multiple steps, alternating between heating and cooling, where heat enters during expansion and leaves during compression.

The efficiency (e) is defined as the net work done over the heat input.
Maximum efficiency (e = 1) is impossible as some heat (Q out) must always be expelled, as defined by the second law of thermodynamics.
The Carnot cycle serves as the theoretical limit for engine efficiency, which is determined strictly by reservoir temperatures.

The Carnot cycle consists of four processes: two isothermal and two adiabatic.
The working substance is an ideal gas, and it operates between high (TH) and low (TL) temperature reservoirs.
Key Stages of the Carnot Cycle:
- Step 1 (Isothermal Expansion): Absorbs heat from the high-temperature reservoir, work done on gas equals absorbed heat.
- Step 2 (Adiabatic Expansion): Gas expands without heat exchange, cooling as it does work.
- Step 3 (Isothermal Compression): Transfers heat to the low-temperature reservoir during compression.
- Step 4 (Adiabatic Compression): Gas is compressed without heat exchange, increasing internal temperature.
Carnot Efficiency Formula:
- Efficiency ( e = 1 - \frac{T_L}{T_H} ), indicating efficiency rises as the lower temperature approaches absolute zero.
The efficiency of any real heat engine will always be less than that of a Carnot engine operating between the same two temperatures, ensuring the limits set by the second law of thermodynamics are respected.