Thermal Equilibrium, Zeroth Law & Concept of Heat and Work
Thermodynamics deals with the macroscopic transformation of heat energy into mechanical work and vice versa. Unlike mechanics where an object is characterized by coordinates like position and momentum, thermodynamics describes macroscopic systems using macroscopic state variables such as pressure (P), volume (V), temperature (T), internal energy (U), and mass or number of moles (n).
1. Thermodynamic Systems & Boundaries
A thermodynamic system is a specified portion of the universe separated from the rest of the universe (the surroundings) by real or imaginary boundaries:
- Open System: Can exchange both energy (heat and work) and matter with its surroundings (e.g., water boiling in an open beaker).
- Closed System: Can exchange energy with its surroundings, but cannot exchange matter (e.g., gas enclosed in a cylinder with a movable piston).
- Isolated System: Cannot exchange either energy or matter with surroundings (e.g., liquid in an ideally insulated, sealed Dewar flask or thermos).
Diathermic Wall
A conducting boundary that allows heat flow between the system and surroundings until thermal equilibrium is established. Example: A thin copper or aluminum plate separating two chambers.
Adiabatic Wall
An insulating boundary that prevents any exchange of heat between the system and surroundings (ΔQ = 0). Example: Thick layers of asbestos, fiberglass, or vacuum flask walls.
2. Thermodynamic Equilibrium
A system is said to be in thermodynamic equilibrium if macroscopic state variables (P, V, T, mass composition) do not change spontaneously with time. It requires three simultaneous equilibria:
- Mechanical Equilibrium: No unbalanced forces within the system or between the system and its surroundings (uniform pressure throughout).
- Chemical Equilibrium: No spontaneous chemical reactions or net transfer of matter from one part of the system to another (uniform chemical composition).
- Thermal Equilibrium: No temperature gradient exists within the system or across conducting boundaries with surroundings.
3. The Zeroth Law of Thermodynamics & Concept of Temperature
Formulated by Ralph H. Fowler in 1931, this law provides the logical basis for the concept and measurement of temperature. It implies the existence of a scalar property called temperature such that:
Temperature is that property of a system which determines whether or not it is in thermal equilibrium with other systems. A thermometer acts as the third reference system C.
4. Internal Energy (U)
The internal energy (U) of a thermodynamic system is the sum total of all microscopic forms of energy of its constituent molecules:
- Kinetic Energy: Translational, rotational, and vibrational kinetic energies of molecules (directly proportional to temperature T).
- Potential Energy: Mutual intermolecular potential energy arising from intermolecular forces (depends on intermolecular spacing, i.e., volume V).
Internal energy is a strictly defined state variable (or state function). In any cyclic process returning to its initial state, ΔUcycle = 0.
5. Work in Thermodynamics
Consider a gas enclosed in a cylinder of cross-sectional area A fitted with a frictionless, movable piston. When the gas expands quasi-statically by a differential displacement dx against external pressure P:
For a finite expansion from initial volume V1 to final volume V2, the total work done by the gas is:
Geometrical Meaning on P-V Indicator Diagram: The work done during any quasi-static process equals the area under the process curve projected onto the volume (V) axis.
- Expansion (V2 > V1): Area is positive ⇒ Work is done by the system (ΔW > 0 in physics).
- Compression (V2 < V1): Volume decreases ⇒ Work is done on the system (ΔW < 0 in physics).
- Cyclic Process: Net work done equals the enclosed area of the loop on the P-V diagram. Clockwise cycle = positive net work (heat engine); Counter-clockwise cycle = negative net work (refrigerator/heat pump).
6. Heat (ΔQ) vs Work (ΔW): Path Variables
Heat and work are modes of energy transfer across boundaries, not forms of energy stored within a system:
| Property | Internal Energy (U) | Heat (Q) & Work (W) |
|---|---|---|
| Nature | State Function (Point function) | Path Function (Process variable) |
| Mathematical Differential | Exact differential (dU) | Inexact differential (δQ, δW) |
| Value in Cyclic Process | ∮ dU = 0 always | ∮ δQ = ∮ δW ≠ 0 in general |
| Physical Meaning | Energy possessed by the system | Energy in transit across the boundary |
In Physics (NCERT):
- ΔQ > 0: Heat entered into the system.
- ΔQ < 0: Heat released/lost by the system.
- ΔW > 0: Work done by the system (expansion: dV > 0).
- ΔW < 0: Work done on the system (compression: dV < 0).
7. Quasi-Static Process
An ideal thermodynamic process that occurs infinitely slowly such that the system departs from thermodynamic equilibrium by only an infinitesimal amount at every intermediate stage. In a quasi-static process:
- The pressure and temperature remain uniform throughout the system at every instant.
- The path of the process can be precisely plotted on a P-V indicator diagram.
- If dissipative effects (such as friction and viscosity) are absent, every quasi-static process is reversible.
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