In thermodynamics, the energy u(s, v) is a function of the entropy, s and volume, v. show that the expressions for pressure (p=-uv) and temperature (t=us) are dictated by the chain rule along with the first law of thermodynamics: du=tds-pdv. now consider the specific case of an ideal monatomic gas with u(s, v)=3/2 nk [ (n/v) exp[s/nk]]2/3 where n is the number of atoms and k is boltzmann’s constant. show that this expression for the energy gives the usual equation of state pv=nkt.
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Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.
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In thermodynamics, the energy u(s, v) is a function of the entropy, s and volume, v. show that the e...
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