Thermodynamics
A clear, first-year engineering guide to temperature, heat, work, energy, and thermodynamic processes
How to use this guide: Build the physical picture first, then use the equations. Thermodynamics becomes
much easier when you keep track of what the system is, what crosses its boundary, and what state it is in.
1. The Big Picture
Thermodynamics is the study of how energy is stored, transferred, and converted. It does not primarily ask
what every molecule is doing. Instead, it describes large-scale quantities such as temperature, pressure,
volume, internal energy, and entropy.
A useful mental model is to imagine a gas trapped inside a piston-cylinder. You can heat the gas, let it
expand, compress it, or allow it to exchange energy with its surroundings. Thermodynamics gives you a
systematic way to calculate what changes.
The central question: Where did the energy go?
2. System, Surroundings, and Boundary
System: the part you choose to study. Surroundings: everything outside it. Boundary: the conceptual or
physical surface separating them.
Three common system types:
System
Mass crosses boundary?
Energy crosses boundary?
Example
Closed
No
Yes
Gas in a sealed piston
Open / control volumeYes
Yes
Turbine, compressor, nozzle
Isolated
No
Idealized perfectly insulated sealed system
No
3. Properties and State
A property describes the condition of a system. Examples include pressure (P), temperature (T), volume (V),
density (ρ), and internal energy (U).
The state is the complete condition needed to describe the system at a given instant. A state variable
depends only on the current state, not on how the system got there.
State functions: P, T, V, U, H, S. Path-dependent quantities: heat Q and work W.
This distinction is extremely important: a system can arrive at the same final state through many different
processes, but the change in a state function is the same.
4. Temperature, Thermal Equilibrium, and the Zeroth Law
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Temperature tells us about the thermal state of a system. If two objects are placed in thermal contact and
eventually stop exchanging net heat, they are in thermal equilibrium.
Zeroth Law: If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal
equilibrium with C. This is what makes temperature measurement meaningful.
5. Pressure and the Ideal Gas
Pressure is force distributed over area: P = F/A. In a gas, pressure results from enormous numbers of
molecular collisions with the container walls.
For an ideal gas:
PV = nRT
P = absolute pressure, V = volume, n = amount in moles, R = 8.314 J/(mol·K), and T = absolute temperature
in kelvin. Always use kelvin in this equation.
6. Heat vs. Temperature
These are not the same thing. Temperature describes the thermal state. Heat is energy transferred because
of a temperature difference.
If you hold a hot metal block and a hot bathtub at the same temperature, they have the same temperature, but
the bathtub can contain much more thermal/internal energy because it contains much more matter.
Heat is commonly represented by Q. By convention in this guide, Q > 0 means heat enters the system and Q <
0 means heat leaves it.
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7. Work
Work is another way energy crosses a system boundary. For a piston, the gas can push against an external
force and move the piston. Energy is transferred through this organized mechanical interaction.
For quasi-equilibrium boundary work:
W = ∫ P dV
On a P–V diagram, the area under the process curve represents boundary work. With the convention used
here, expansion generally gives positive work done by the system; compression gives negative work.
8. The First Law of Thermodynamics
The first law is conservation of energy applied to a thermodynamic system.
∆U = Q − W
Here W means work done by the system. So energy entering as heat increases internal energy unless some
of it leaves as work.
Example: A gas receives 500 J of heat and does 200 J of work on a piston. Then ∆U = 500 − 200 = 300 J.
The gas retains 300 J more internal energy.
9. Internal Energy
Internal energy U is the microscopic energy stored within the system, including molecular kinetic and
interaction energies. In many introductory problems, you do not need to calculate every molecular
contribution. You only need the change ∆U.
For an ideal gas, internal energy depends only on temperature. Therefore, if an ideal gas returns to its original
temperature, its internal energy returns to its original value, even if its pressure and volume followed a
complicated path.
For a simple ideal gas with constant specific heat:
∆U = n C■ ∆T
10. Specific Heat and Sensible Heating
Specific heat tells you how much energy is needed to change the temperature of a unit amount of material.
For mass-based calculations:
Q = m c ∆T
where m is mass, c is specific heat capacity, and ∆T is temperature change. This relation is useful when there
is no phase change and the specific heat can be treated as approximately constant.
11. Enthalpy
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Enthalpy is defined as:
H = U + PV
For flowing systems such as turbines, compressors, pumps, and heat exchangers, enthalpy appears naturally
because moving fluid carries internal energy plus the energy associated with pushing fluid into and out of a
control volume.
For an ideal gas with constant specific heats:
∆H = n C■ ∆T
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12. Common Thermodynamic Processes
A process describes how a system moves from one state to another. The most useful special cases are
defined by what remains constant.
Process
Constant quantity
Key idea
Isothermal
T
Temperature stays constant
Isobaric
P
Pressure stays constant
Isochoric
V
Volume stays constant
Adiabatic
Q=0
No heat transfer
Isothermal ideal-gas process: T is constant, so ∆U = 0. From the first law, Q = W.
Isochoric process: V is constant, so boundary work W = ∫P dV = 0. Therefore ∆U = Q.
Adiabatic process: Q = 0. Therefore ∆U = −W for a closed system using the sign convention here.
13. The Second Law of Thermodynamics
The first law tells us that energy is conserved. It does not tell us which energy transformations are naturally
possible. The second law adds direction.
For example, heat naturally flows from a hotter object to a colder one. A refrigerator can move heat from cold
to hot, but it requires work input.
Entropy S is the property used to quantify the direction and irreversibility associated with thermodynamic
processes.
For a reversible process:
dS = δQ■■■ / T
For an isolated system, entropy cannot decrease. Real processes are generally irreversible, so entropy
generation is positive.
14. Heat Engines and Refrigerators
A heat engine receives heat from a high-temperature reservoir, produces some net work, and rejects the
remaining heat to a low-temperature reservoir.
Its thermal efficiency is:
η = W■■■ / Q■ = 1 − Q■/Q■
A refrigerator works in the opposite practical direction: it uses work to remove heat from a cold space and
reject heat to the surroundings.
15. The Carnot Limit
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A reversible Carnot engine operating between hot and cold reservoirs has the maximum theoretical efficiency
for those two reservoir temperatures:
η■Carnot■ = 1 − T■/T■
Temperatures must be absolute temperatures. Real engines have lower efficiency because real processes
contain irreversibilities such as friction, finite temperature differences, mixing, and pressure losses.
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16. A Reliable Problem-Solving Method
Step 1 — Define the system. Decide exactly what you are analyzing.
Step 2 — Identify the states. List known P, V, T, mass, composition, etc.
Step 3 — Identify the process. Is it isothermal, isobaric, isochoric, adiabatic, or something else?
Step 4 — Choose the energy balance. For a closed system, start with ∆U = Q − W unless another
convention is explicitly being used.
Step 5 — Apply the equation of state. For an ideal gas, PV = nRT.
Step 6 — Check units and signs. Use kelvin for thermodynamic temperature and absolute pressure where
required.
Step 7 — Ask whether the answer makes physical sense. This catches many mistakes.
17. Worked Example: Heating a Gas
An ideal gas contains 2.0 mol and is heated from 300 K to 400 K in a rigid container. Assume C■ = 20.8
J/(mol·K). Find the change in internal energy and the heat transferred.
1. The container is rigid, so V is constant. Therefore W = 0.
2. Calculate internal-energy change: ∆U = nC■∆T = (2.0)(20.8)(100) = 4160 J.
3. First law: ∆U = Q − W. Since W = 0, Q = ∆U = 4160 J.
Physical interpretation: all of the heat entering the gas increases its internal energy because the rigid walls
prevent boundary work.
18. Common Mistakes
• Confusing heat with temperature.
• Using °C instead of K in PV = nRT or Carnot equations.
• Forgetting the sign convention for work.
• Treating Q as a property stored inside an object. Heat is energy in transit.
• Assuming ∆U depends on the path for an ideal gas. It does not; U is a state function.
• Using a closed-system equation for an open control volume without accounting for mass flow.
19. Quick Formula Sheet
Concept
Equation
Pressure
P = F/A
Ideal gas
PV = nRT
First law, closed system
∆U = Q − W
Boundary work
W = ∫P dV
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Sensible heating
Q = mc∆T
Internal energy, ideal gas
∆U = nC■∆T
Enthalpy
H = U + PV
Ideal-gas enthalpy change
∆H = nC■∆T
Entropy, reversible
dS = δQ■■■/T
Heat-engine efficiency
η = W■■■/Q■
Carnot efficiency
η = 1 − T■/T■
20. Practice Questions
1. A gas absorbs 800 J of heat and does 300 J of work. What is ∆U?
2. Why is the work zero for a rigid closed container?
3. An ideal gas is heated at constant temperature. What happens to its internal energy?
4. Why must temperature be expressed in kelvin in the ideal-gas law?
5. Explain the difference between an isothermal and an adiabatic process.
6. A heat engine receives 1000 J from a hot reservoir and rejects 600 J. Find its efficiency.
7. Why can no real heat engine operating between two fixed temperatures be more efficient than the Carnot
limit?
Answer Check
1. 500 J 2. No change in volume, so ∫P dV = 0 3. It stays constant for an ideal gas
absolute and the gas law uses that scale 5. Isothermal: constant T; adiabatic: Q = 0
efficiency of reversible and irreversible heat engines.
4. Thermodynamic temperature is
6. 40% 7. The second law limits the
Final mental model
Think of thermodynamics as energy bookkeeping plus direction. The first law tracks where energy goes.
Properties describe the state. Heat and work describe energy crossing the boundary. The second law explains
why real processes have a preferred direction and why useful machines have fundamental limits.
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