Helium zero-point entropy

We cannot measure the absolute internal energy U or enthalpy H because the zero of energy is arbitrary. As a result, we are usually only interested in determining changes in these properties (At/ and A.H) during a process. However, it is possible to determine the absolute entropy of a substance. This is because of the third law of thermodynamics, which states that the entropy of a pure substance in its thermodynamically most stable form is zero at the absolute zero of temperature, independent of pressure. For the vast majority of substances, the thermodynamically most stable form at 0 K is a perfect crystal. An important exception is helium, which remains liquid, due to its large quantum zero-point motion, at 0 K for pressures below about 10 bar. 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

To resolve the viscosity paradox, assume that at the lambda point all the fluid is normal fluid with a normal viscosity, and at absolute zero all the fluid is superfluid with zero viscosity. In the thin channel experiment described above, only the superfluid atoms, which have zero entropy and do not interact, can flow through the slit. On the other hand, the oscillating disk is damped by the normal fluid and thus accounts for the shape of the viscosity curve below the lambda point. The flow of helium II through very thin channels is accompanied by two very interesting thermal effects called the thermomechanical effect and the mechanocaloric effect. ... 

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