10: The First Law of Thermodynamics

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10.1: Overview of Classical Thermodynamics
Joule was able to show that work and heat can have the same effect on matter – a change in temperature! It would then be reasonable to conclude that heating, as well as doing work on a system will increase its energy content, and thus it’s ability to perform work in the surroundings. This leads to an important construct of the First Law of Thermodynamics: The capacity of a system to do work is increased by heating the system or doing work on it.
10.2: All Dilute Gases Behave Ideally
Gases behave according to the ideal gas law when interactions between the gas molecules and the container as well as the size of the particles can be ignored. At low pressures and high temperatures since the gas occupies a large volume, the volume occupied by the constituents of the gas become even more insignificant in comparison. Thus real gases approach ideal behavior at low \(P\) and high \(T\).
10.3: van der Waals and Redlich-Kwong Equations of State
The van der Waals Equation of State is an equation relating the density of gases and liquids to the pressure, volume, and temperature conditions. The Redlich–Kwong equation of state is an empirical, algebraic equation that relates temperature, pressure, and volume of gases. It is generally more accurate than the van der Waals equation and the ideal gas equation at temperatures above the critical temperature.
10.4: Pressure-Volume Work
Work in general is defined as a product of a force FFF and a path element dsdsds. In the case of a cylinder, the movement of the piston is constrained to one direction, the one in which we apply pressure (\(P\) being force \(F\) per area \(A\)). We can therefore introduce the area of the piston, \(A\), and forget about the vectorial nature of force. This form of work is called pressure-volume (\(PV\)) work, and it plays an important role in the development of our theory.
10.5: Work and Heat are not State Functions
Heat and work are both path functions: they depend on the path taken. In order to calculate the heat transfer or work being done on/by a system, the path taken must be known.
10.6: Work and Heat Have a Simple Molecular Interpretation
The internal energy of a system, \(dU\), is exchanged with the system's surroundings thought work and heat.
10.7: Energy is a State Function
Unlike heat and work, energy is a state function. That is, it is independent of the path taken. Any path can be used to calculate the change in energy between two states.
10.8: Heat Capacity is a Path Function
10.9: An Adiabatic Process is a Process in which No Energy as Heat is Transferred
Work is a path function as it always depends on the path taken, even if it is done reversibly.
10.10: The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion
In an adiabatic process, no heat transfer occurs. During the adiabatic expansion of a gas, the internal energy of the gas is converted to work being done by the system, decreasing the temperature of the gas.
10.11: Enthalpy is a State Function
Enthalpy is the energy transferred as heat in an isobaric process when on P-V work is involved.
10.12: Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition
10.13: Enthalpy Changes for Chemical Equations are Additive
As enthalpy and energy are state functions we should expect additivity of U and H when we study chemical reactions. This additivity is expressed in Hess's Law. The additivity has important consequences and the law finds wide spread application in the prediction of heats of reaction. The reverse reaction has the negative enthalpy of the forward one. If we can do a reaction in two steps we can calculate the enthalpy of the combined reaction by adding them up.
10.14: Heats of Reactions Can Be Calculated from Tabulated Heats of Formation
Reaction enthalpies are important, but difficult to tabulate. However, because enthalpy is a state function, it is possible to use Hess’ Law to simplify the tabulation of reaction enthalpies. Hess’ Law is based on the addition of reactions. By knowing the reaction enthalpy for constituent reactions, the enthalpy of a reaction that can be expressed as the sum of the constituent reactions can be calculated.
10.15: The Temperature Dependence of ΔH
It is often required to know thermodynamic functions (such as enthalpy) at temperatures other than those available from tabulated data. Fortunately, the conversion to other temperatures isn’t difficult.
10.E: The First Law of Thermodynamics (Exercises)

Thumbnail: A thermite reaction using iron(III) oxide. The sparks flying outwards are globules of molten iron trailing smoke in their wake. (CC SA-BY 3.0; Nikthestunned).