The First Law of Thermodynamics is a fundamental principle that expresses the conservation of energy in thermodynamic processes. It states that the change in internal energy of a system equals the heat added to the system minus the work done by the system. This law establishes that energy cannot be created or destroyed, only transferred or converted from one form to another. The internal energy U represents the total energy contained within the system (kinetic and potential energy of molecules), heat Q represents energy transfer due to temperature difference, and work W represents energy transfer through mechanical processes. This principle is the foundation for analyzing all thermodynamic processes and is essential for understanding engines, refrigerators, power plants, and countless other energy systems.
Historical Context: The law was developed over the 19th century, with key contributions from scientists like James Prescott Joule, who experimentally demonstrated the mechanical equivalent of heat in the 1840s, and Rudolf Clausius, who provided a clear mathematical formulation in 1850. It solidified the universal principle of energy conservation, a cornerstone of modern physics.
The First Law of Thermodynamics is a restatement of the law of conservation of energy, applied to thermodynamic systems. It is fundamentally a scalar relationship that equates the change in a system's internal energy to the net heat transfer and work done.
| Property | Details |
|---|---|
| Nature | A scalar relationship, as it involves energy, heat, and work, which are all scalar quantities. |
| SI Units | The standard unit for all terms in the equation (change in internal energy ΔU, heat Q, and work W) is the Joule (J). |
| Sign Convention | The signs are critical: <ul><li><strong>Q > 0</strong>: Heat is added to the system.</li><li><strong>W > 0</strong>: Work is done by the system on its surroundings.</li><li><strong>ΔU > 0</strong>: The internal energy of the system increases.</li></ul> |
| Conservation Law | This law is a direct application of the principle of conservation of energy, stating that the total energy of an isolated system is constant. |
| Dimensional Formula | All terms (ΔU, Q, W) share the dimensions of energy, which is [M L^2 T^-2]. |
| Symbol | Quantity | SI Unit | Description |
|---|---|---|---|
| \( \Delta U \) | Change in Internal Energy | Joule (J) | The change in the total energy contained within a system. It is a state function. |
| \( Q \) | Heat | Joule (J) | Energy transferred due to a temperature difference. Positive when heat is added to the system. |
| \( W \) | Work | Joule (J) | Energy transferred through mechanical means. Positive when work is done by the system. |
| \( W_{on} \) | Work Done On System | Joule (J) | Alternative convention for work. Positive when work is done on the system (\(W_{on} = -W\)). |
| \( dU \) | Infinitesimal Change in Internal Energy | Joule (J) | An exact differential, representing a small change in a state function. |
| \( \delta Q, \delta W \) | Infinitesimal Heat and Work | Joule (J) | Inexact differentials, as heat and work are path-dependent functions. |
The First Law of Thermodynamics is not derived from more fundamental principles but is itself a postulate based on the universal Law of Conservation of Energy. It is a generalization of countless experimental observations, most notably those by James Joule, which established a direct equivalence between mechanical work and heat.
The conceptual derivation starts with the principle that energy in an isolated system is conserved. For a non-isolated system, any change in its total internal energy (\(\Delta U\)) must be equal to the net energy that crosses its boundary. Energy can cross the boundary in two forms: heat (\(Q\)) and work (\(W\)).
We can state the energy balance as:
By defining \(Q\) as heat added *to* the system and \(W\) as work done *by* the system on its surroundings, we arrive at the mathematical formulation of the First Law:
The First Law of Thermodynamics, expressed as ΔU = Q - W, can be simplified for several specific types of thermodynamic processes defined by what quantity is held constant.
| Type / Case | Description | When to Use |
|---|---|---|
| Isochoric Process | A process occurring at constant volume (ΔV = 0). Since no volume change occurs, the work done is zero (W = 0). The law simplifies to <strong>ΔU = Q</strong>. | Used for systems heated or cooled in a rigid, sealed container where expansion or contraction is not possible. |
| Isobaric Process | A process occurring at constant pressure (ΔP = 0). Work is done as the volume changes (W = PΔV). The law is expressed as <strong>ΔU = Q - PΔV</strong>. | Used for systems that can expand or contract against a constant external pressure, such as a gas in a cylinder with a movable piston. |
| Isothermal Process | A process occurring at constant temperature (ΔT = 0). For an ideal gas, the internal energy depends only on temperature, so ΔU = 0. The law becomes <strong>Q = W</strong>. | Used for analyzing slow processes where the system has time to exchange heat with a thermal reservoir to maintain a constant temperature. |
| Adiabatic Process | A process where no heat is exchanged with the surroundings (Q = 0). The law simplifies to <strong>ΔU = -W</strong>. Any work done by the system comes from its internal energy. | Used to model very fast processes (e.g., sound wave propagation, engine compression stroke) or for systems that are extremely well-insulated. |
The First Law of Thermodynamics is fundamental to numerous fields of science and engineering:
Refrigerator: A refrigerator is a practical application of the First Law. An external compressor does work on a refrigerant gas, increasing its internal energy and temperature. This hot gas then releases heat to the room's environment. The cooled, expanded gas inside the fridge absorbs heat from the food (increasing its internal energy again), keeping the food cold. The entire cycle is a continuous process of energy transfer governed by \(\Delta U = Q - W\).
Pumping a Bicycle Tire: When you use a manual pump to inflate a tire, you are doing work on the air inside the pump. This work compresses the air, increasing its internal energy. Since the pumping action is rapid, there is little time for heat to escape (an approximately adiabatic process), so the increase in internal energy manifests as a noticeable increase in temperature. This is why the base of a bicycle pump gets hot during use.
Human Metabolism: The human body is a thermodynamic system. The chemical energy stored in food represents the internal energy input. The body converts this energy, performing work through muscle contractions and releasing heat to maintain a constant body temperature. The First Law dictates that the energy from food must be fully accounted for as work done, heat lost, and changes in the body's stored energy (like fat).
In the International System of Units (SI), all terms in the First Law of Thermodynamics—internal energy, heat, and work—are measured in Joules (J). This ensures consistency in the energy balance.
| Quantity | Symbol | SI Unit | Dimensional Formula |
|---|---|---|---|
| Internal Energy | U | Joule (J) | [M][L]²[T]⁻² |
| Heat | Q | Joule (J) | [M][L]²[T]⁻² |
| Work | W | Joule (J) | [M][L]²[T]⁻² |
Dimensional analysis confirms the consistency of the law: \([M][L]^2[T]^{-2} = [M][L]^2[T]^{-2} - [M][L]^2[T]^{-2}\). All quantities must have dimensions of energy.
The formula is ΔU = Q - W. It calculates the change in a system's internal energy (ΔU) by accounting for the net heat (Q) added to the system and the work (W) done by the system.
In the equation ΔU = Q - W, ΔU represents the change in internal energy, Q is the heat transferred to the system, and W is the work done by the system. All three quantities are measures of energy and have SI units of Joules (J).
This law is used to analyze energy transformations in thermodynamic processes like those in heat engines, refrigerators, and chemical reactions. It is applied to specific processes such as isothermal (constant temperature), adiabatic (no heat transfer), isobaric (constant pressure), and isochoric (constant volume) changes.
A common error is incorrectly assigning the sign for work. In the convention ΔU = Q - W, work (W) is positive when the system expands and does work on its surroundings, causing internal energy to decrease. Work is negative when the surroundings do work on the system (compression), which increases its internal energy.
In an internal combustion engine, the combustion of fuel adds heat (Q) to the gas in a cylinder, increasing its internal energy (ΔU). This expanding gas then does work (W) on a piston, converting thermal energy into the mechanical energy that powers the vehicle, perfectly illustrating the law's principles.
The First Law of Thermodynamics is a specific statement of the universal principle of Conservation of Energy. It asserts that the total energy of an isolated system is constant, meaning energy can only be transferred or converted into different forms (internal energy, heat, or work), not created or destroyed.