First Law of Thermodynamics Study Pack
Kibin's free study pack on First Law of Thermodynamics includes a 5-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.
Last updated May 27, 2026
First Law of Thermodynamics Study Guide
Master the First Law of Thermodynamics by working through ΔU = Q − W, internal energy as a state function, and how heat and work transfer across system boundaries. Covers isothermal, adiabatic, isobaric, and isochoric processes and energy conservation applied to expanding gases.
Key Takeaways
- •The First Law of Thermodynamics states that the change in a system's internal energy equals the heat added to the system minus the work done by the system: ΔU = Q − W.
- •Internal energy is the total microscopic kinetic and potential energy stored within a system; it is a state function that depends only on the current condition of the system, not on how it got there.
- •Heat (Q) and work (W) are energy transfer processes that occur at the boundary between a system and its surroundings — they are not stored quantities.
- •When a gas expands against an external pressure, it does positive work on its surroundings, which reduces the system's internal energy if no heat is added to compensate.
- •The First Law is a restatement of conservation of energy applied to thermodynamic systems, meaning energy cannot be created or destroyed — only transferred or converted between forms.
- •Different thermodynamic processes (isothermal, adiabatic, isochoric, isobaric) each impose a specific constraint that simplifies how ΔU, Q, and W relate to one another.
The Core Principle: Energy Conservation in Thermodynamic Systems
The First Law of Thermodynamics extends the classical principle of energy conservation to systems that exchange heat and do mechanical work, establishing a precise accounting framework for every energy interaction.
The Law as an Energy Balance Equation
- •The mathematical statement of the First Law is ΔU = Q − W, where ΔU is the change in internal energy, Q is the net heat flowing into the system, and W is the net work done by the system on its surroundings.
- •If Q is positive, energy enters the system as heat; if Q is negative, energy leaves as heat.
- •If W is positive, the system expends energy by doing work on the surroundings (e.g., a gas pushing a piston outward); if W is negative, the surroundings do work on the system.
Sign Convention Consistency
- •Some textbooks write the First Law as ΔU = Q + W, where W is defined as work done on the system rather than by the system — the physics is identical, but the sign of W flips depending on the convention used.
- •In the physics convention (ΔU = Q − W), work done by the system is positive, which aligns naturally with mechanical expansion problems.
- •Always identify which sign convention is in use before solving a problem, because mixing conventions produces errors.
What the First Law Prohibits
- •A perpetual motion machine of the first kind — a device that produces net work output without any energy input — is impossible because it would require ΔU to increase without any Q or W input, violating energy conservation.
- •The First Law does not, however, specify the direction in which energy transformations happen spontaneously; that is the domain of the Second Law of Thermodynamics.
Internal Energy: What Is Actually Stored in a System
Internal energy is the thermodynamic property that sits at the center of the First Law, yet it is frequently misunderstood because it cannot be measured directly — only its changes can be observed.
Microscopic Origins of Internal Energy
- •Internal energy (U) is the sum of all microscopic kinetic energies (translational, rotational, and vibrational motion of molecules) and potential energies (intermolecular attractions and repulsions) within the system.
- •For an ideal monatomic gas, intermolecular potential energy is negligible, so internal energy depends almost entirely on the translational kinetic energy of the atoms, which is directly proportional to absolute temperature: U = (3/2)nRT.
- •For real gases and liquids, intermolecular potential energy also contributes to U, making the relationship between U and temperature more complex.
Internal Energy as a State Function
- •Internal energy is a state function, meaning its value is determined entirely by the current macroscopic state of the system (temperature, pressure, volume, and composition) — not by the path the system took to reach that state.
- •Because U is a state function, ΔU between two states is always the same regardless of whether the system was heated, compressed, or underwent a chemical reaction to get there.
- •Heat and work, by contrast, are path functions — their values depend on the specific process used, which is why Q and W individually vary across different processes even when ΔU is the same.
Heat and Work: The Two Modes of Energy Transfer
Heat and work are the only two mechanisms by which energy can cross the boundary of a closed system, and understanding the distinction between them is essential for applying the First Law correctly.
Heat as a Thermal Energy Transfer
- •Heat (Q) is energy that flows across a system boundary driven by a temperature difference between the system and its surroundings — it is not a quantity that a system 'contains.'
- •Heat transfer occurs via conduction (direct molecular collisions through matter), convection (bulk fluid movement carrying thermal energy), and radiation (electromagnetic waves, which require no medium).
- •Once heat enters a system and becomes part of the random molecular motion, it is indistinguishable from the internal energy already present.
Mechanical Work Done by an Expanding or Compressed Gas
- •For a gas exerting pressure P against a movable boundary (such as a piston) that moves through a small displacement, the incremental work done by the gas is dW = P dV.
- •For a finite process at constant pressure, this simplifies to W = PΔV, where ΔV is the change in volume.
- •When a gas expands (ΔV > 0) at constant pressure, W is positive — the gas does work on the piston, reducing internal energy unless heat compensates.
- •When a gas is compressed (ΔV < 0), W is negative — the surroundings do work on the gas, increasing internal energy.
Other Forms of Work in Thermodynamic Systems
- •Work is not limited to pressure-volume work; electrical work, surface tension work, and shaft work can also transfer energy across a system boundary.
- •In all cases, work requires a macroscopic, organized force acting through a displacement — this distinguishes it conceptually from the disorganized, random-motion energy transfer that defines heat.
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Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.
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What is the mathematical statement of the First Law of Thermodynamics using the physics convention?
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The First Law of Thermodynamics
Explain the First Law of Thermodynamics in your own words. What does the equation ΔU = Q − W mean, and what fundamental principle does it express?
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