Energy, Heat, Work, and Thermodynamic Systems
In thermodynamics, energy is the capacity to do work or transfer heat, heat (q) is energy transferred because of a temperature difference, work (w) is energy transferred by a force acting through a distance, and the system is the part of the universe chosen for study. In brief: when a gas expands from 2.0 L to 5.0 L against a constant pressure of 1.0 atm, it does work w = −PΔV = −3.0 L·atm, which is about −304 J.
Thermochemistry begins with a clear vocabulary. Before you can calculate how much energy a reaction releases, you must know what you are describing (the system), how it exchanges energy with its surroundings and which sign convention is in use. This article defines these terms, explains the sign conventions and state functions, and works through examples of pressure–volume work and energy units.
What is energy?
Energy is usually defined as the capacity to do work or to produce heat. Two main forms are important in chemistry:
- Kinetic energy is the energy of motion, Ek = ½mv2. The thermal energy of a substance is the total kinetic energy of its particles.
- Potential energy is stored energy that depends on position or composition. In chemistry, the energy stored in chemical bonds and in the attractions between particles is called chemical energy.
The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another or transferred. For example, in the combustion of fuel, chemical energy is converted to thermal energy and, in an engine, partly to mechanical work.
What are systems and surroundings?
The system is the part of the universe under study, for instance the reacting mixture in a flask. Everything else is the surroundings, and the boundary between them may be real or imaginary. Systems are classified according to what can cross the boundary.
| System | Exchanges matter? | Exchanges energy? | Example |
|---|---|---|---|
| Open | Yes | Yes | Boiling water in an open pot, a living cell |
| Closed | No | Yes | A sealed flask in a water bath |
| Isolated | No | No | A well-insulated thermos (approximately), the universe |
What are heat and work?
Heat (q) flows from a hotter object to a colder one until their temperatures are equal. It is a way of transferring energy, and not a substance contained in objects. Work (w) is the energy transferred when a force moves an object, for example when a gas expands and pushes a piston. For a gas expanding or compressing at constant external pressure:
w = −Pext × ΔV
The minus sign means that when the system expands (ΔV > 0), it does work on the surroundings and loses energy. Other forms of work include electrical work, which is important in batteries, and work against surface tension.
What is the sign convention?
Chemistry uses the system’s point of view: a quantity is positive when energy enters the system and negative when it leaves.
| Quantity | Positive (+) | Negative (−) |
|---|---|---|
| Heat, q | Heat flows into the system (endothermic) | Heat flows out of the system (exothermic) |
| Work, w | Work done on the system (compression) | Work done by the system (expansion) |
| Internal energy, ΔU | System gains energy | System loses energy |
Some older engineering textbooks define work as positive when it is done by the system. Always check the convention before using a formula.
What are state functions?
A state function depends only on the present state of the system, and not on how that state was reached. Internal energy (U), enthalpy (H), entropy (S), Gibbs energy (G), temperature, pressure and volume are state functions. Heat and work are not: they are path functions, because the amounts depend on the way in which the change is carried out. The change in a state function is the difference between the final and initial values, ΔX = Xfinal − Xinitial. This is the reason why Hess’s law works.
Which units are used for energy?
- Joule (J): the SI unit, 1 J = 1 kg·m2/s2 = 1 N·m. The kilojoule (kJ) is 1000 J.
- Calorie (cal): the thermochemical calorie is defined as exactly 4.184 J. The Calorie (capital C) on food labels is a kilocalorie, 1 Cal = 1000 cal = 4184 J.
- Liter-atmosphere (L·atm): a unit of pressure–volume work, 1 L·atm = 101.325 J.
- Electronvolt (eV): used for single particles, 1 eV = 1.602 × 10−19 J.
Worked examples
Example 1: expansion work
A gas expands from 2.0 L to 5.0 L against a constant external pressure of 1.0 atm. The work is w = −1.0 atm × (5.0 − 2.0) L = −3.0 L·atm. In joules: −3.0 × 101.325 = −304 J. The negative sign shows that the system has done work on the surroundings.
Example 2: energy of a snack
A snack bar is labeled as 250 Calories. The energy in kilojoules is 250 × 4.184 = 1046 kJ, which is about 1.05 MJ. If an adult uses about 100 W (100 J/s) at rest, this energy corresponds to 1,046,000 / 100 = 10,460 s, or about 2.9 hours.
Example 3: kinetic energy
A 70 kg cyclist moving at 5.0 m/s has a kinetic energy of ½ × 70 × 5.02 = 875 J. This is only a fraction of the energy of a few grams of fat.
Example 4: classifying systems
A sealed, uninsulated bottle of soda on a table can exchange heat with the room but not matter, so it is a closed system. When the cap is opened, CO2 escapes, and the bottle becomes an open system.
How did the concept of energy develop?
Early scientists considered heat to be a fluid called caloric. In 1798, Benjamin Thompson (Count Rumford) observed that boring cannon barrels produced seemingly unlimited heat, which was hard to explain with a fluid. In the 1840s James Prescott Joule measured the mechanical equivalent of heat with paddle-wheel experiments, Julius Robert Mayer proposed the equivalence of heat and work, and Hermann von Helmholtz formulated the conservation of energy in 1847. The SI unit of energy is named after Joule.
Which mistakes are common?
- Mixing up signs: work done by the system is negative, and heat absorbed is positive.
- Thinking that heat is stored in an object: an object has internal energy, and heat is energy in transit.
- Forgetting unit conversions: L·atm must be converted to J, and Calories to joules.
- Treating q and w as state functions: only their sum, ΔU, is path-independent.
- Confusing Calorie and calorie: the food Calorie is 1000 times larger.