Thermodynamics
An exploration of energy, heat, work, and entropy. Discover the fundamental laws that govern energy conversion and the direction of natural processes, from the smallest engines to the entire universe.
The Zeroth Law & Thermal Equilibrium
The surprisingly fundamental law that makes temperature a useful concept.
Defining Temperature
The Zeroth Law of Thermodynamics states: If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
While it sounds obvious, this law is crucial. It means we can create a third system (a thermometer) to measure the property of “temperature.” If our thermometer reads the same for two separate objects, we know that no heat will flow if they are brought into contact.
$$ If \ T_A = T_C \ and \ T_B = T_C, \ then \ T_A = T_B $$The First Law of Thermodynamics
A statement of the conservation of energy for thermal systems.
Internal Energy, Heat, and Work
The First Law states that energy cannot be created or destroyed, only converted from one form to another. The change in the internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system.
$$ \Delta U = Q – W $$This law is a restatement of the conservation of energy principle, specifically for thermodynamic systems.
Heat Engines & Refrigerators
Devices that convert thermal energy into mechanical work, and vice versa.
The Engine Cycle
A heat engine operates in a cycle, taking heat (Q_h) from a high-temperature source, converting part of it into mechanical work (W), and expelling the rest as waste heat (Q_c) to a low-temperature sink.
The efficiency (η) of a heat engine is the ratio of the work done to the heat absorbed. The maximum possible efficiency, known as the Carnot efficiency, depends only on the temperatures of the hot and cold reservoirs.
$$ \eta = \frac{W}{Q_h} = 1 – \frac{Q_c}{Q_h} \quad \Rightarrow \quad \eta_{Carnot} = 1 – \frac{T_c}{T_h} $$Refrigerators & Heat Pumps
A refrigerator is essentially a heat engine running in reverse. It uses external work (W) to extract heat (Q_c) from a cold reservoir and transfer it to a hot reservoir (Q_h).
Instead of efficiency, we measure its effectiveness with the Coefficient of Performance (COP). For a refrigerator, this measures how much heat is removed per unit of work done.
$$ COP_{ref} = \frac{Q_c}{W} $$The Second Law & Entropy
A measure of disorder and the fundamental asymmetry of time.
The Arrow of Time
The Second Law of Thermodynamics can be stated in several ways, but it fundamentally sets a direction for natural processes. One key statement is: The total entropy of an isolated system can only increase over time. It can never decrease.
Entropy (S) is a measure of the randomness, disorder, or number of microscopic arrangements (microstates) available to a system. Processes naturally proceed in a direction that increases the total entropy of the universe.
$$ \Delta S \ge \int \frac{dQ}{T} $$This is why heat spontaneously flows from hot to cold, and why it’s easier to break an egg than to un-break it.
Thermodynamic Processes
Four key pathways for a system to change its state, visualized on a P-V diagram.
Isobaric Process
A process occurring at constant pressure. As the gas is heated, it expands and does work.
\( \Delta P = 0 \)
\( W = P \Delta V \)
Isochoric Process
A process occurring at constant volume. Since the volume doesn’t change, no work is done.
\( \Delta V = 0 \)
\( W = 0; \quad \Delta U = Q \)
Isothermal Process
A process occurring at constant temperature. Internal energy of an ideal gas does not change.
\( \Delta T = 0 \)
\( \Delta U = 0; \quad Q = W \)
Adiabatic Process
A process where no heat is exchanged with the surroundings. This happens in well-insulated systems or very fast processes.
\( Q = 0 \)
\( \Delta U = -W \)
Interactive P-V Diagram
Visualizing thermodynamic processes for an ideal gas. Hover over the cycle to see details.
Real-World Applications
Thermodynamics is not just theoretical; it powers our modern world.
Internal Combustion Engines
The engine in your car is a prime example of a heat engine. It burns fuel (a high-temperature source) to expand a gas, pushing pistons to create mechanical work, and expels exhaust heat.
Refrigerators & Air Conditioners
These devices are heat engines running in reverse. They use work (from electricity) to move heat from a cold space (inside the fridge) to a warmer space (the room), defying the natural direction of heat flow.
Power Plants
Whether fossil fuel, nuclear, or geothermal, most large-scale power plants use thermodynamics. They heat water into high-pressure steam, which expands to turn turbines (doing work) that generate electricity.
Solved Numerical Problems
Apply the principles you’ve learned to solve practical problems.
Problem 1: The First Law
Question: A gas in a cylinder absorbs 2000 J of heat. As it expands, it does 500 J of work on its surroundings. What is the change in the internal energy of the gas?
Formula Used: \( \Delta U = Q – W \)
Identify the given values: Heat added Q = +2000 J. Work done by the system W = +500 J.
Substitute the values into the First Law equation.
\( \Delta U = 2000 \, J – 500 \, J \)
Problem 2: Engine Efficiency
Question: A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. What is its maximum theoretical efficiency?
Formula Used: \( \eta_{Carnot} = 1 – \frac{T_c}{T_h} \)
Identify the reservoir temperatures: T_h = 500 K, T_c = 300 K. (Note: Temperatures must be in Kelvin).
Substitute the temperatures into the Carnot efficiency formula.
\( \eta = 1 – \frac{300 \, K}{500 \, K} = 1 – 0.6 \)