This paper presents an alternative generalization of classical thermoelasticity, discussing restrictions on constitutive equations using an entropy production inequality proposed by Green and Laws. The work is closely related to Müller's but yields more explicit results. The theory is linearized and a uniqueness theorem is stated. It is shown that the linear heat conduction tensor is symmetric and that the theory allows for "second sound" effects, in agreement with Müller. The paper introduces the basic equations of thermoelasticity, including balance equations for a single phase continuum. These equations involve stress, heat flux, and entropy, and are expressed in terms of spatial and reference coordinates. The paper also presents an entropy inequality derived from Müller's work and suggested by Green and Laws, which allows for non-zero heat supply and body forces. This inequality leads to a condition that ensures the validity of the entropy production. The paper discusses the implications of this entropy inequality for linear thermoelasticity, showing that the heat conduction tensor is symmetric and that the theory allows for "second sound" effects. It also provides sufficient conditions for the uniqueness of solutions to the initial and mixed boundary-value problems in linear thermoelasticity. The results are compared with those of Müller, showing agreement in many respects but with more explicit expressions for the stress tensor, heat conduction vector, and entropy in terms of two scalar functions. The paper concludes with a discussion of the implications of these results for the theory of thermoelasticity.This paper presents an alternative generalization of classical thermoelasticity, discussing restrictions on constitutive equations using an entropy production inequality proposed by Green and Laws. The work is closely related to Müller's but yields more explicit results. The theory is linearized and a uniqueness theorem is stated. It is shown that the linear heat conduction tensor is symmetric and that the theory allows for "second sound" effects, in agreement with Müller. The paper introduces the basic equations of thermoelasticity, including balance equations for a single phase continuum. These equations involve stress, heat flux, and entropy, and are expressed in terms of spatial and reference coordinates. The paper also presents an entropy inequality derived from Müller's work and suggested by Green and Laws, which allows for non-zero heat supply and body forces. This inequality leads to a condition that ensures the validity of the entropy production. The paper discusses the implications of this entropy inequality for linear thermoelasticity, showing that the heat conduction tensor is symmetric and that the theory allows for "second sound" effects. It also provides sufficient conditions for the uniqueness of solutions to the initial and mixed boundary-value problems in linear thermoelasticity. The results are compared with those of Müller, showing agreement in many respects but with more explicit expressions for the stress tensor, heat conduction vector, and entropy in terms of two scalar functions. The paper concludes with a discussion of the implications of these results for the theory of thermoelasticity.