What Is the First Law of Thermodynamics?
The First Law of Thermodynamics is one of the most fundamental principles in all of science: energy cannot be created or destroyed, only converted from one form to another. In chemistry, this law governs every reaction, every phase change, and every physical process. It tells us that the total energy of an isolated system remains constant over time.
Expressed mathematically, the First Law states:
ΔU = q + w
Where ΔU is the change in internal energy of the system, q is the heat transferred to the system, and w is the work done on the system.
Internal Energy
Internal energy (U) is the total energy stored within a chemical system — including the kinetic energy of moving molecules, the potential energy stored in chemical bonds, and the energy associated with intermolecular forces. We cannot measure the absolute value of internal energy, but we can measure changes in internal energy (ΔU) through heat and work.
When a system absorbs heat from its surroundings, q is positive (endothermic). When a system releases heat, q is negative (exothermic). These signs follow the perspective of the system, not the surroundings.
Work in Chemical Systems
In chemistry, the most common form of work is pressure-volume (PV) work — the work done when a gas expands or contracts against an external pressure. The formula is:
w = −P_ext × ΔV
When a gas expands (ΔV > 0) against an external pressure, the system does work on the surroundings, so w is negative — energy leaves the system as work. When a gas is compressed (ΔV < 0), work is done on the system, so w is positive.
Enthalpy: A Practical Convenience
Most chemical reactions occur at constant pressure (open to the atmosphere), not constant volume. Under constant pressure, chemists use a related quantity called enthalpy (H):
H = U + PV
The change in enthalpy at constant pressure is:
ΔH = q_p
This means ΔH equals the heat exchanged at constant pressure — which is exactly what we measure in a typical laboratory calorimeter. Enthalpy is convenient because it automatically accounts for the PV work of expansion.
- Exothermic reactions: ΔH < 0 (heat released to surroundings; combustion of methane, CH₄ + 2O₂ → CO₂ + 2H₂O)
- Endothermic reactions: ΔH > 0 (heat absorbed from surroundings; dissolving ammonium nitrate in water)
Hess's Law
Because enthalpy is a state function (its value depends only on the current state of the system, not on the path taken to get there), we can use Hess's Law to calculate enthalpy changes for reactions that are difficult to measure directly.
Hess's Law states that if a reaction can be expressed as the sum of two or more other reactions, its enthalpy change is the sum of the enthalpy changes of those reactions. This powerful tool lets chemists build up complex thermochemical equations from simpler ones.
Example: To find ΔH for C(s) + ½O₂(g) → CO(g), combine known reactions for complete combustion of carbon and combustion of carbon monoxide.
Calorimetry: Measuring Heat
Calorimetry is the experimental technique used to measure heat changes in chemical reactions. A bomb calorimeter (constant volume) measures ΔU directly, while a coffee-cup calorimeter (constant pressure, open to atmosphere) measures ΔH.
The heat measured in a calorimeter is calculated as:
q = m × c × ΔT
Where m is mass, c is the specific heat capacity of the substance, and ΔT is the temperature change. Water's specific heat capacity (4.184 J/g·°C) makes it an excellent calorimetric medium.
Real-World Applications
- Nutrition labels: The "calories" in food are actually kilocalories (kcal) — energy measured by burning food in a bomb calorimeter
- Rocket propulsion: Engineers calculate ΔU and ΔH for fuel combustion reactions to design efficient engines
- Industrial chemistry: Reaction enthalpy determines heating and cooling requirements for large-scale chemical manufacturing
- Metabolic processes: Cellular respiration (C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O) releases ~2,800 kJ/mol, powering all biological activity
Summary
The First Law of Thermodynamics is the bookkeeper of the universe — it ensures that every joule of energy is accounted for. Whether energy flows as heat or work, the total never changes. Understanding ΔU, q, w, and ΔH gives chemists the tools to predict how much energy a reaction releases or requires, which is essential for everything from drug design to battery development.