Maurice A. Biot's paper "Thermoelasticity and Irreversible Thermodynamics" presents a unified treatment of thermoelasticity using methods from irreversible thermodynamics. The paper introduces a "thermoelastic potential" as a generalized free energy and a new dissipation function based on the time derivative of entropy displacement. It formulates the general laws of thermoelasticity in a variational form along with a minimum entropy production principle, leading to equations of the Lagrangian type. The concept of thermal force is introduced through a virtual work definition. Heat conduction problems are formulated using matrix algebra and mechanics, leading to the property that entropy density obeys a diffusion-type law. General solutions of thermoelasticity equations are given using the Papkovitch-Boussinesq potentials. Examples are presented, and the generalized coordinate method is used to calculate thermoelastic internal damping of elastic bodies. The paper also discusses the analogy between thermoelasticity and the theory of elasticity of porous materials, showing that the equations are the same with temperature playing the role of fluid pressure. The paper extends the treatment to anisotropic media and dynamics, and applies the variational method to derive dynamical equations for thermoelastic media. The paper concludes with an application to heat conduction, showing how the methods can be used to solve classical heat conduction problems. The paper also discusses the concept of generalized free energy and the rate of entropy production, and shows how the minimum entropy production principle applies to thermoelasticity and heat conduction. The paper introduces generalized coordinates and admittance matrices, leading to the treatment of practical thermal problems by matrix algebra in analogy with stress and vibration analysis methods. The concept of generalized thermal force is defined by a virtual displacement method as in mechanics. The paper also discusses the propagation of entropy as a diffusion process and its application to anisotropic media. The paper concludes with a discussion of thermoelastic damping and its experimental verification, showing how the generalized coordinate method can be used to evaluate thermoelastic damping of crystals in piezoelectric oscillators.Maurice A. Biot's paper "Thermoelasticity and Irreversible Thermodynamics" presents a unified treatment of thermoelasticity using methods from irreversible thermodynamics. The paper introduces a "thermoelastic potential" as a generalized free energy and a new dissipation function based on the time derivative of entropy displacement. It formulates the general laws of thermoelasticity in a variational form along with a minimum entropy production principle, leading to equations of the Lagrangian type. The concept of thermal force is introduced through a virtual work definition. Heat conduction problems are formulated using matrix algebra and mechanics, leading to the property that entropy density obeys a diffusion-type law. General solutions of thermoelasticity equations are given using the Papkovitch-Boussinesq potentials. Examples are presented, and the generalized coordinate method is used to calculate thermoelastic internal damping of elastic bodies. The paper also discusses the analogy between thermoelasticity and the theory of elasticity of porous materials, showing that the equations are the same with temperature playing the role of fluid pressure. The paper extends the treatment to anisotropic media and dynamics, and applies the variational method to derive dynamical equations for thermoelastic media. The paper concludes with an application to heat conduction, showing how the methods can be used to solve classical heat conduction problems. The paper also discusses the concept of generalized free energy and the rate of entropy production, and shows how the minimum entropy production principle applies to thermoelasticity and heat conduction. The paper introduces generalized coordinates and admittance matrices, leading to the treatment of practical thermal problems by matrix algebra in analogy with stress and vibration analysis methods. The concept of generalized thermal force is defined by a virtual displacement method as in mechanics. The paper also discusses the propagation of entropy as a diffusion process and its application to anisotropic media. The paper concludes with a discussion of thermoelastic damping and its experimental verification, showing how the generalized coordinate method can be used to evaluate thermoelastic damping of crystals in piezoelectric oscillators.