Isothermal and Adiabatic Elastic Tensors
  The adiabatic elastic modulus is often useful in the high frequency response of materials. Unfortunately, it can be much more difficult to directly measure the adiabatic elastic modulus of material than the isothermal elastic modulus. We derive the relationship between the adiabatic and isothermal elastic tensors from the first law of thermodynamics. 
Michael J. Waters and Andrew W. Bielawski
cond-mat.mtrl-sci