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Introduction Thermodynamic Systems Internal Energy The First Law of Thermodynamics Work in Thermodynamics Important Thermodynamic Processes Specific Heat Capacity The Second Law of Thermodynamics Entropy Heat Engines The Carnot Cycle Refrigerators and Heat Pumps The Third Law of Thermodynamics Practical Applications Why Thermodynamics MattersThermodynamics is the study of heat, work, temperature, and their relationship to energy, entropy, and the physical properties of matter and radiation.
While mechanics deals with the motion of objects and forces, thermodynamics examines energy transformations and the fundamental limitations on those transformations. It addresses questions like: Why does heat always flow from hot to cold? Why can't we build a perfect engine? What determines whether a process occurs spontaneously?
Thermodynamics emerged from practical needs—improving steam engines during the Industrial Revolution—but evolved into one of physics' most profound theories with universal applicability.
A thermodynamic system is the portion of the universe under study. Everything outside is the surroundings. The boundary separates the system from its surroundings.
No exchange of energy or matter with surroundings.
Example: ideal insulated container (approximation)
Energy can cross the boundary, but matter cannot.
Example: sealed piston cylinder
Both energy and matter can cross the boundary.
Example: boiling water in an open pot
A thermodynamic process describes how a system changes from one equilibrium state to another.
Definition: The internal energy (U) of a system is the total energy contained within the system, including kinetic energy of particle motion and potential energy of particle interactions.
For an ideal gas (no intermolecular forces), internal energy is purely kinetic:
U = (3/2)nRT
where n is the amount of substance in moles, R is the gas constant, and T is the absolute temperature.
Internal energy is a state function — it depends only on the current state (T, P, V, n), not on how that state was reached.
Change in internal energy: ΔU = U_final - U_initial
ΔU can be positive (energy added to the system) or negative (energy removed from the system).
ΔU = Q - W
ΔU = change in internal energy (J)
Q = heat transferred to the system (J)
W = work done by the system (J)
Sign conventions (using ΔU = Q - W):
This is essentially conservation of energy applied to thermodynamic systems. Energy isn't created or destroyed, only transformed between forms and transferred between systems and their surroundings.
Example: A gas absorbs 500 J of heat and expands, doing 300 J of work on the surroundings. Find ΔU.
ΔU = Q - W = 500 - 300 = 200 J (internal energy increases by 200 J)
W = ∫P dV
For constant pressure (isobaric process): W = PΔV
Geometrically, work equals the area under the P-V curve.
Example: A gas at constant pressure 200 kPa expands from 0.5 m³ to 1.2 m³. Calculate the work done by the gas.
W = PΔV = (200,000)(1.2 - 0.5) = (200,000)(0.7) = 140,000 J = 140 kJ
Q = mcΔT (specific heat capacity)
Q = nCΔT (molar specific heat capacity)
For gases, specific heat depends on whether pressure or volume is held constant:
For ideal gas: C_P = C_V + R
The ratio γ = C_P/C_V is important for adiabatic processes.
Heat cannot spontaneously flow from a colder to a hotter object without external work being done.
No heat engine can convert heat completely into work with 100% efficiency. Some heat must be exhausted to a cold reservoir.
The entropy of an isolated system never decreases; it either increases (irreversible process) or remains constant (reversible process).
The second law explains why many processes are irreversible. You can convert work entirely into heat (rub hands together), but you can't convert heat entirely into work without some heat being wasted.
This establishes a fundamental directionality to natural processes, sometimes called the "arrow of time."
ΔS = Q/T (for reversible heat transfer)
SI unit: J/K
Entropy (S) is a measure of the disorder or randomness of a system. More precisely, it quantifies the number of microscopic configurations corresponding to a macroscopic state.
The second law states: ΔS_universe ≥ 0
For isolated systems: ΔS ≥ 0
Examples of entropy increase:
A heat engine is a device that converts thermal energy into mechanical work through cyclic processes.
Operating principle:
Energy conservation: W = Q_H - Q_C
Thermal efficiency: η = W/Q_H = 1 - Q_C/Q_H
Example: A heat engine absorbs 1000 J from a hot reservoir and exhausts 600 J to a cold reservoir. Find efficiency and work output.
W = 1000 - 600 = 400 J
η = 400/1000 = 0.40 = 40%
η_Carnot = 1 - T_C/T_H
Temperatures must be in Kelvin.
The Carnot engine is a theoretical ideal heat engine operating between two thermal reservoirs with maximum possible efficiency.
The Carnot cycle consists of four reversible processes:
Example: A Carnot engine operates between 500 K and 300 K. Find the maximum efficiency.
η_Carnot = 1 - 300/500 = 1 - 0.6 = 0.4 = 40%
No engine operating between these temperatures can exceed 40% efficiency.
COP_refrigerator = Q_C/W = Q_C/(Q_H - Q_C)
COP_Carnot = T_C/(T_H - T_C)
A refrigerator is a heat engine running in reverse. Work input removes heat from the cold reservoir and exhausts heat to the hot reservoir.
Higher COP means a more efficient refrigerator (more cooling per unit work).
Heat pumps use the same principle for heating buildings, extracting heat from cold outside air and delivering it inside.
S → 0 as T → 0 K
Statement: As the temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.
This establishes an absolute entropy scale and implies absolute zero is unattainable in finite steps (temperatures can approach but never reach 0 K).
Thermodynamics establishes fundamental limits on what's possible. No matter how clever engineering becomes, certain efficiencies cannot be exceeded. These aren't technological limitations — they're laws of nature.
The second law explains why perpetual motion machines are impossible, why we can't extract unlimited work from ocean thermal energy, and why disorder tends to increase.
Understanding thermodynamics is essential for energy engineering, climate science, chemistry, biology, and even information theory and cosmology. It's one of physics' most broadly applicable theories, with principles that have stood unchanged for over 150 years.