When nano and macro structures made by the same material are connected to each other under a temperature gradient, thermosize effects appear.
Density distribution of ideal gases confined in a finite domain is not uniform even in thermodynamic equilibrium.
Particle number and internal energy exhibit an intrinsic discreteness which allows them to take only some definite values. Thermodynamic properties of an ideal Fermi gas have either stepwise or oscillatory nature.
Even an infinitesimally thin wall immersed in a domain filled by a gas, has a nonzero effective thickness. Gas pressure acting on the effective cross section of movable wall causes an outward quantum force.
Dimensional transitions in thermodynamic properties occur in momentum space due to quantum confinement.
We derive analytical expressions for thermodynamic state functions considering quantum size and shape effects.
Analytical expressions for Seebeck coefficient under quantum size effects are derived with a good agreement with experimental and numerical results.
Size dependencies of thermal and electrical conductivities are different, the Lorenz number becomes size and shape dependent and deviations from the Wiedemann–Franz law is expected at nanoscale due to QSE.