Why is internal energy a function of temperature and volume? $u=f(T,V)$. In my reasoning, I can only understand that internal energy is a function of Temperature, because it changes directly with Temperature. If temperature raises, $u$ raises, if $T$ decreases, $u$ decreases.

What about enthalpy? Why is it a function of temperature and pressure? $h=f(T,p)$

  • 3
    $\begingroup$ That may be true for an ideal gas but it's not true in general... $\endgroup$ – lemon Apr 22 '17 at 16:32
  • $\begingroup$ From the phase rule, it takes two independent degrees of freedom to specify the thermodynamic equilibrium state of a single phase, single component substance. $\endgroup$ – Chet Miller Apr 22 '17 at 19:12
  • $\begingroup$ It may be worth looking up 'state variables' and 'extensivity'. $\endgroup$ – MPath Apr 23 '17 at 8:43

Internal energy includes both the kinetic energy and the potential energy (of interaction) of the molecules. As the specific volume gets smaller, the molecules squeeze together more, and the potential energy (and thus the internal energy) changes. As the molecules get further apart, the potential energy makes less and less of a contribution, and the internal energy is determined solely by the temperature (kinetic energy).


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