First Law of Thermodynamics
The First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another, making it a statement of conservation of energy applied to thermodynamic systems. For any process, the change in internal energy of a system equals the heat added to the system minus the work done by the system on its surroundings. This principle underpins the analysis of engines, refrigerators, and all energy-conversion devices in engineering and science.
Key Formula
ΔU = Q - W
LaTeX: \Delta U = Q - W
| Symbol | Meaning | Unit |
|---|---|---|
| ΔU | Change in internal energy of the system | J |
| Q | Heat added to the system (positive when absorbed) | J |
| W | Work done by the system on surroundings | J |
Worked Example
Problem
A gas in a cylinder absorbs 500 J of heat from a reservoir and simultaneously does 200 J of work by expanding against a piston. What is the change in internal energy of the gas?
Solution
Step 1: Identify known quantities. Q = +500 J (heat absorbed), W = +200 J (work done by gas). Step 2: Apply the First Law: ΔU = Q − W. Step 3: Substitute values: ΔU = 500 J − 200 J = 300 J.
Answer
ΔU = 300 J (internal energy increases by 300 J)
Sign Convention for the First Law of Thermodynamics
| Quantity | Positive (+) | Negative (−) | Effect on ΔU |
|---|---|---|---|
| Heat (Q) | Heat absorbed by system | Heat released by system | Q > 0 increases ΔU |
| Work (W) | Work done by system | Work done on system | W > 0 decreases ΔU |
| ΔU | Internal energy rises | Internal energy falls | Depends on Q and W |
| Isothermal process | ΔU = 0 | Q = W | Temperature constant |
| Adiabatic process | Q = 0 | ΔU = −W | No heat exchange |
Interactive Tools
PhET Gas Properties Simulation
Interactive simulation to explore heat, work, and internal energy in gases
Open ToolKhan Academy – First Law of Thermodynamics
Video lessons and practice problems on thermodynamic laws
Open ToolWolfram Alpha Thermodynamics Calculator
Compute thermodynamic quantities and verify energy balance calculations
Open Tool
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Related Terms
Second Law of Thermodynamics
The Second Law of Thermodynamics states that in any spontaneous process, the total entropy of an isolated system can only increase or remain constant, never decrease. This gives thermodynamics a preferred direction of time, explaining why heat flows from hot to cold, why mechanical energy converts irreversibly to heat, and why perpetual motion machines of the second kind are impossible. It is the thermodynamic basis for the arrow of time and sets fundamental efficiency limits on all heat engines.
Entropy
Entropy is a thermodynamic state function that quantifies the degree of disorder, randomness, or the number of microstates available to a system at a given macrostate. Macroscopically, it is defined via the Clausius inequality as the ratio of reversible heat exchange to absolute temperature; microscopically, Boltzmann's formula connects it to the number of microscopic configurations. Entropy always increases in irreversible processes in isolated systems, driving systems toward equilibrium and explaining the thermodynamic arrow of time.
Enthalpy
Enthalpy is a thermodynamic state function defined as the sum of the internal energy of a system and the product of its pressure and volume, representing the total heat content of a system at constant pressure. At constant pressure, the change in enthalpy equals the heat exchanged between the system and its surroundings, making it the central quantity in calorimetry, chemical reactions, and engineering heat-exchange calculations. Positive ΔH indicates an endothermic process (heat absorbed), while negative ΔH indicates an exothermic process (heat released).
From Greek "thermos" (heat) and "dynamis" (power). The law was formulated in the mid-19th century through the combined work of Julius Robert von Mayer (1842), James Prescott Joule (1843), and Hermann von Helmholtz (1847), who each independently established the principle of energy conservation.