First Law of Thermodynamics

The First Law of Thermodynamics — also known as the Law of Conservation of Energy — states that energy can be converted from one form to another, but it can never be created or destroyed. The total energy of the universe remains constant. If a system loses energy, the surroundings must gain it, and vice versa:

ΔE_system = −ΔE_surroundings

Applied to a system alone, the First Law is written as:

ΔE = q + w

where q is the heat added to or removed from the system, and w is the work done by or on the system. (You may also see this written as ΔE = q − w, depending on sign convention — both forms convey the same physics. This article uses ΔE = q + w throughout.)

Key Takeaways

• First Law of Thermodynamics: energy is conserved; ΔE = q + w for a system.

• Heat (q) and work (w) each have a sign convention based on the system's perspective; PV work (w = −PΔV) governs expansion/contraction work.

• Heat transfers by conduction (molecular collisions), convection (fluid motion), or radiation (electromagnetic waves, no medium needed).

• Heat capacity links heat to temperature change (q = mcΔT); water's high specific heat capacity (4.18 J/g·K) makes it an effective coolant.

• Heating curves show temperature rising within a phase but plateauing during phase transitions (q = mL), as energy goes into breaking intermolecular forces.

• The four thermodynamic processes — isothermal, adiabatic, isobaric, isochoric — each hold a different quantity constant and produce a distinct P-V diagram shape.

Heat and Work

Heat (q) is the flow of energy that results from a temperature difference between two objects. Heat always flows from the hotter object to the colder one. Heat is not the same as temperature — temperature measures the kinetic energy of particles, while heat refers to the transfer of that energy between objects. Heat is not energy itself, but one of the two ways energy can be transferred (the other being work).

Work (w) is the second way energy transfers. In physics, work is the result of a force acting over a distance:

w = F · d · cos(θ)

MCAT Callout — Heat and Work Sign Convention: From the system's perspective — heat added to the system: q is positive; heat removed from the system: q is negative; surroundings do work on the system: w is positive; system does work on the surroundings: w is negative.

Pressure-Volume (PV) Work

A special type of work common in chemical systems is PV work — the work done as a system expands or contracts under pressure, such as in a piston. It's given by:

w = −PΔV

• When a gas expands, ΔV is positive, so w is negative — the system does work on the surroundings.

• When a gas contracts, ΔV is negative, so w is positive — the surroundings do work on the system.

A useful conversion factor: 101.3 J = 1 L·atm.

Heat Transfer Mechanisms

For energy to transfer between objects, they must be in thermal contact. Heat flows in three distinct ways:

• Conduction — direct transfer of energy from molecule to molecule through collisions. This is the primary mode of heat transfer in solids, where molecules are tightly packed. Example: a metal spoon left in a hot pot of soup warms up as heat conducts along the handle.

• Convection — transfer of heat through the physical motion of a fluid. Warmer, less dense regions of a fluid rise while cooler, denser regions sink, creating a circulation pattern that carries heat along. Example: water heating in a pot, with hot water rising from the bottom and cooler water sinking from the surface.

• Radiation — transfer of energy through electromagnetic waves, requiring no medium. Unlike conduction and convection, radiation can transfer heat across a vacuum. Example: the warmth of sunlight reaching Earth through space.

Heat Capacity

Heat and temperature aren't the same, but they're closely related through heat capacity — the amount of heat required to raise a substance's temperature by 1°C.

• Specific heat capacity is heat capacity per gram: the heat needed to raise 1 gram of a substance by 1°C (or 1 K).

• Molar heat capacity is the heat needed to raise 1 mole of a substance by 1°C.

The heat transferred during a temperature change is calculated with:

q = mcΔT

where m is mass, c is specific heat capacity, and ΔT is the temperature change. Because ΔT is the same whether measured in Celsius or Kelvin, c can be expressed in either unit.

One especially important value: the specific heat capacity of water is 4.18 J/g·K (equivalently, 4.18 J/g·°C). This high value lets water absorb and store large amounts of heat without large temperature swings — making it an effective coolant and a key player in environmental temperature regulation.

Heating Curves and Phase Changes

A heating curve graphs a substance's temperature (y-axis) against the heat added to it (x-axis), visualizing phase changes and the energy involved in each transition.

As heat is added, temperature rises within a single phase — but during a phase transition, temperature remains constant even as heat continues to be absorbed. A typical solid-to-gas heating curve moves through:

1. Solid phase — temperature rises steadily.

2. Melting — temperature holds constant at the melting point while the solid absorbs heat and converts to liquid; the energy required is the heat of fusion.

3. Liquid phase — temperature rises again.

4. Vaporization — temperature holds constant at the boiling point while the liquid absorbs heat and converts to gas; the energy required is the heat of vaporization.

5. Gas phase — temperature rises further with additional heat.

MCAT Callout — Why Temperature Plateaus During a Phase Transition: During melting or vaporization, added energy goes toward breaking the intermolecular forces holding particles in their current phase — not toward increasing particle kinetic energy. Since temperature is a measure of kinetic energy, it stays flat until the phase change is complete.

Two formulas cover the full heating curve:

• During temperature changes: q = mcΔT (m = mass, c = specific heat capacity, ΔT = temperature change).

• During phase changes: q = mL, where L is the latent heat (heat of fusion or vaporization).

Specific heat capacity and latent heat are both properties specific to a given substance and phase.

Thermodynamic Processes

Four fundamental thermodynamic processes describe how a system behaves under different constraints, typically visualized on a Pressure-Volume (P-V) diagram:

• Isothermal — constant temperature. Heat added to the system is exactly balanced by work done by the system. Because PV = nRT, at constant T, pressure and volume are inversely proportional, producing a hyperbolic P-V curve. Example: slow compression or expansion of a gas that exchanges heat with its surroundings.

• Adiabatic — no heat exchange with the surroundings (the system is insulated). Any change in internal energy comes solely from work, so temperature changes as the gas expands or compresses. The P-V curve is steeper than an isothermal curve. Example: the compression stroke in an internal combustion engine, or rapid release of air from a bicycle pump.

• Isobaric — constant pressure, changing volume. Represented by a horizontal line on a P-V diagram. Heat added changes both internal energy and work at constant pressure. Example: heating a gas in a piston that's free to expand or contract while pressure stays constant.

• Isochoric — constant volume, no work done (since volume doesn't change). Represented by a vertical line on a P-V diagram. Heat added directly changes internal energy, which changes pressure. Example: heating a gas in a rigid, sealed container.

Common MCAT Mistakes

• Mixing up the sign of w between the two ΔE conventions. Whether w is "work done on" or "work done by" the system flips its sign depending on which form of the First Law (ΔE = q + w vs. ΔE = q − w) a passage uses. Always check which convention is in play before assigning a sign.

• Confusing heat and temperature. Heat is energy in transit between objects; temperature is a measure of a substance's average kinetic energy. A small object at high temperature can transfer less total heat than a large object at a lower temperature.

• Forgetting that temperature is constant during a phase change. Students often try to apply q = mcΔT across a melting or boiling plateau — but during a phase transition, ΔT = 0 and the correct formula is q = mL instead.

• Mislabeling adiabatic as "no temperature change." Adiabatic means no heat exchange (q = 0), not no temperature change — an adiabatically compressed gas can heat up significantly even though q = 0, because ΔE comes entirely from work.

MCAT-Style Concept Check

Question: A gas is compressed adiabatically inside an insulated cylinder. Which of the following best describes the energy changes occurring in the system?

• A) q is positive, w is positive, and ΔE increases

• B) q is zero, w is positive, and ΔE increases

• C) q is zero, w is negative, and ΔE decreases

• D) q is negative, w is zero, and ΔE decreases

Answer: B

Explanation: "Adiabatic" means no heat is exchanged with the surroundings, so q = 0. Compression means the surroundings do work on the gas, so w is positive (by the ΔE = q + w convention used in this article). With q = 0 and w positive, ΔE = w, which is positive — the internal energy of the gas increases, consistent with the gas heating up as it's compressed.

FAQ

What is the First Law of Thermodynamics in simple terms?

It states that energy cannot be created or destroyed, only converted between forms or transferred between a system and its surroundings — expressed for a system as ΔE = q + w.

What's the difference between heat and work?

Both are ways energy transfers into or out of a system. Heat (q) is energy transfer driven by a temperature difference; work (w) is energy transfer resulting from a force acting over a distance, such as a gas expanding against a piston.

Why does temperature stay constant during melting or boiling?

Because the heat added during a phase transition goes into breaking intermolecular forces rather than increasing particle kinetic energy — and temperature is a measure of that kinetic energy, so it doesn't change until the phase change finishes.

What's the difference between an isothermal and an adiabatic process?

An isothermal process holds temperature constant while heat is exchanged with the surroundings to balance the work done. An adiabatic process allows no heat exchange at all, so any work done changes the system's temperature directly.