Learning Objectives
- Understand thermal equilibrium and the zeroth law of thermodynamics
- Learn the first law of thermodynamics and its applications
- Study thermodynamic processes: isothermal, adiabatic, isobaric, isochoric
- Understand the second law and concept of entropy
- Learn about heat engines, refrigerators, and Carnot cycle
Key Concepts
Thermodynamic System and State Variables
A thermodynamic system is separated from surroundings by a boundary. State variables (P, V, T, n) describe the state of the system.
Equation of state (ideal gas): PV = nRT, R = 8.314 J/(mol·K).
Zeroth Law of Thermodynamics
If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law defines temperature.
First Law of Thermodynamics
ΔU = Q - W (Change in internal energy = Heat added - Work done by system)
Sign convention: Q > 0 (heat absorbed), W > 0 (work done by system).
Internal energy (U): A state function. For ideal gas, U depends only on temperature: U = nCᵥT.
Work done by gas: W = ∫P dV = area under P-V curve.
Thermodynamic Processes
Isothermal Process (T = constant): PV = constant. W = nRT ln(V₂/V₁). ΔU = 0, so Q = W.
Adiabatic Process (Q = 0): PVᵞ = constant. TVᵞ⁻¹ = constant. W = (P₁V₁ - P₂V₂)/(γ-1) = nCᵥ(T₁-T₂). ΔU = -W.
Isobaric Process (P = constant): W = PΔV. Q = nCₚΔT.
Isochoric Process (V = constant): W = 0. Q = ΔU = nCᵥΔT.
γ = Cₚ/Cᵥ. For monatomic gas: γ = 5/3. Diatomic: γ = 7/5. Cₚ - Cᵥ = R.
Second Law of Thermodynamics
Kelvin-Planck Statement: No heat engine can convert all absorbed heat into work (100% efficiency is impossible).
Clausius Statement: Heat cannot spontaneously flow from a colder body to a hotter body without external work.
Heat Engines
A device that converts heat into work in a cyclic process.
Efficiency: η = W/Q₁ = 1 - Q₂/Q₁, where Q₁ = heat absorbed, Q₂ = heat rejected.
Carnot Engine
An ideal, reversible engine with maximum possible efficiency between two temperatures.
Carnot cycle: Two isothermal + two adiabatic processes.
Carnot efficiency: η = 1 - T₂/T₁ (T in Kelvin). Efficiency depends only on temperatures of source and sink.
No real engine can be more efficient than a Carnot engine operating between the same temperatures.
Refrigerator and Heat Pump
A refrigerator transfers heat from a cold body to a hot body using external work.
Coefficient of Performance: COP = Q₂/W = Q₂/(Q₁ - Q₂) = T₂/(T₁ - T₂)
Summary
Thermodynamics deals with heat, work, and internal energy. The zeroth law defines temperature. The first law (energy conservation) relates heat, work, and internal energy change. Different processes (isothermal, adiabatic, isobaric, isochoric) have distinct characteristics. The second law limits the efficiency of heat engines. The Carnot engine gives maximum efficiency η = 1 - T₂/T₁.
Important Terms
- State Function: Depends only on the state, not on the path (e.g., U, T, P, V)
- Path Function: Depends on the process/path (e.g., Q, W)
- Isothermal: Process at constant temperature
- Adiabatic: Process with no heat exchange
- Entropy: Measure of disorder; ΔS = Q/T for reversible process
- Carnot Cycle: Most efficient thermodynamic cycle
Quick Revision
- First law: ΔU = Q - W; Internal energy is a state function
- Isothermal: PV = const, W = nRT ln(V₂/V₁)
- Adiabatic: PVᵞ = const, W = nCᵥ(T₁-T₂)
- Cₚ - Cᵥ = R; γ = Cₚ/Cᵥ (5/3 monatomic, 7/5 diatomic)
- Carnot efficiency: η = 1 - T₂/T₁
- COP of refrigerator = Q₂/(Q₁ - Q₂)