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First Law of Thermodynamics

1850

Julius Robert von Mayer
James Prescott Joule
Hermann von Helmholtz
Rudolf Clausius

(generated image for illustration only)

The First Law is a statement of the conservation of energy. It posits that the change in a closed system’s internal energy (\(\Delta U\)) is equal to the heat supplied to the system (\(Q\)) minus the work done by the system on its surroundings (\(W\)). The governing equation is \(\Delta U = Q – W\). This law links heat, work, and internal energy, establishing heat as a form of energy transfer.

The First Law of Thermodynamics generalized the principle of conservation of energy, which was previously known in mechanics, to include heat. Its formulation was a major step in physics, as it definitively refuted the prevailing caloric theory, which considered heat a weightless fluid. Experiments by James Joule in the 1840s, which demonstrated the mechanical equivalent of heat, were crucial in establishing that heat and work are mutually convertible.

The law introduces internal energy (\(U\)) as a state function, meaning its value depends only on the current state of the system, not on how it got there. In contrast, heat (\(Q\)) and work (\(W\)) are path-dependent process quantities. The law’s differential form is \(dU = \delta Q – \delta W\). For a cyclic process, where the system returns to its initial state, the change in internal energy is zero (\(\Delta U = 0\)), so the net heat supplied equals the net work done. This principle is the basis for all heat engines. The law also implies the impossibility of a perpetual motion machine of the first kind—a machine that produces work without any energy input.

Closed-Loop Product Development, Energy, Enthalpy, Heat Treatment, Mechanical Engineering, Process Optimization, Quality Management, Thermodynamics

UNESCO Nomenclature: 2212

– Thermodynamics, statistical physics, and condensed matter

Type

Abstract System

Disruption

Revolutionary

Usage

Widespread Use

Precursors

Sadi Carnot’s analysis of heat engines and thermodynamic cycles
James Joule’s experiments on the mechanical equivalent of heat
rejection of the caloric theory of heat
principle of conservation of energy in mechanics as formulated by Leibniz and others

Applications

heat engines (internal combustion, steam turbines)
refrigerators, air conditioners, and heat pumps
chemical reaction analysis (enthalpy calculations)
power plant design and efficiency analysis
nutritional calorimetry for calculating food energy (calories)

Patents:

Potential Innovations Ideas

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Related to: first law, conservation of energy, internal energy, heat, work, thermodynamics, enthalpy, closed system, state function, perpetual motion.

Historical Context

19th century laboratory with thermodynamic instruments and Mayer's relation equations.

Mayer’s Relation (thermodynamics)

Mayer's relation connects the specific heats of a perfect gas to the specific gas constant (\(R_s\)). The relation is \(c_p - c_v = R_s\). For molar specific heats (\(C_p\) and \(C_v\)), the relation is \(C_p - C_v = R\), where \(R\) is the universal gas constant. This shows that \(c_p\) is always greater than \(c_v\).

19th-century laboratory with physicists studying energy conservation principles.

Conservation of Energy

A fundamental principle stating that the total energy of an isolated system remains constant over time. Energy can neither be created nor destroyed, only transformed from one form to another, such as from potential to kinetic energy. In classical mechanics, for systems with only conservative forces, the total mechanical energy \(E = T + V\) is conserved.

Laboratory setup for measuring viscosity of fluids at varying temperatures in thermodynamics.

Temperature Dependence of Viscosity

For a Newtonian fluid, viscosity is a function of temperature and pressure but not shear rate. In liquids, viscosity decreases significantly as temperature increases because higher thermal energy allows molecules to overcome cohesive intermolecular forces more easily. Conversely, in gases, viscosity increases with temperature as more frequent molecular collisions at higher speeds lead to greater momentum transfer.

First Law of Thermodynamics

Chemist conducting experiments with catalysts in a vintage laboratory setting, 1850.

Catalyst on Chemical Equilibrium

A catalyst increases the rate of both the forward and reverse reactions equally by providing an alternative reaction pathway with a lower activation energy. While a catalyst allows a system to reach equilibrium much faster, it does not change the position of the equilibrium itself. The equilibrium concentrations of reactants and products, and the value of the equilibrium constant K, remain unchanged.

19th-century chemist measuring gas volumes illustrating the Ideal Gas Law in thermodynamics.

Ideal Gas Law (Molar Form)

The ideal gas law is the equation of state for a hypothetical ideal gas, approximating the behavior of many gases under various conditions. The molar form relates pressure (\(P\)), volume (\(V\)), amount of substance in moles (\(n\)), and absolute temperature (\(T\)) via the universal gas constant (\(R\)): \(PV = nRT\).

Laboratory apparatus for measuring vapor pressure and temperature in thermodynamics.

Clausius-Clapeyron Relation

The Clausius-Clapeyron relation describes the relationship between pressure and temperature for a substance at a phase transition, such as liquid and vapor. For water vapor, it shows that saturation vapor pressure increases exponentially with temperature. The approximate form is \(\frac{dp}{dT} = \frac{L}{T(V_v - V_l)} \approx \frac{L p}{R_v T^2}\), where L is latent heat.

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Demonstration of Joule heating in a vintage laboratory with electric appliances.

Joule Heating and Electric Power

Joule heating, or ohmic heating, is the phenomenon where heat is produced by an electric current passing through a conductor. The rate of heat generation, or power dissipated (\(P\)), is given by Joule's first law, \(P = VI\). By combining this with Ohm's law, the power can be expressed as \(P = I^2 R\) or \(P = \frac{V^2}{R}\).

Internal Energy and Enthalpy of a Perfect Gas

For a perfect gas, the internal energy (\(U\)) and enthalpy (\(H\)) are functions of temperature only. Their changes are given by \(\Delta U = m c_v \Delta T\) and \(\Delta H = m c_p \Delta T\), where \(c_v\) and \(c_p\) are the specific heats at constant volume and pressure, respectively, and are assumed to be constant.

Researcher testing viscoelastic properties of synthetic polymer in a laboratory.

Viscoelasticity

Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials, like a rubber band, strain when stretched and quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both.

Scientist measuring sublimation in a vintage laboratory, thermodynamics study.

Enthalpy of Sublimation

The enthalpy of sublimation, \(\Delta H_{\text{sub}}\), is the heat required to convert one mole of a substance from solid to gas at a given temperature and pressure. According to Hess's Law, since enthalpy is a state function, this energy change is the sum of the enthalpy of fusion (\(\Delta H_{\text{fus}}\)) and the enthalpy of vaporization (\(\Delta H_{\text{vap}}\)).