Question

For many substances, there exists a temperature $T_{tr}$. and a pressure ptr at which all the three phases of a substance (gaseous, liquid, and solid) are in equilibrium. These temperature and pressure are known as the triple point. For example,$T_{tr}={0.0075}^{\circ }C$ and $p_{tr}=4.58mm$ Hg for water. The latent heat of vaporization of water at the triple point is $q=2.48\times {10}^{3}kJ/kg$, and the latent heat of fusion of ice is $\lambda =0.34\times {10}^{3}kJ/kg$.
Find the latent heat $v$ of sublimation (i.e. a direct transition from the solid to the gaseous state) of water at the triple point.

Answer 1

Let us consider a cycle embracing the triple point:$A\to B\to C\to A$(Fig.). The following phase transitions occur in turn: melting $\to$ vaporization $\to$ condensation of gas directly into the solid. Provided that the cycle infinitely converges
to the triple point, we obtain from the first law of thermodynamics for the mass m of a substance
$m\lambda +mq-mv=0$
since the work of the system during a cycle is zero, there is no inflow of heat from outside, and hence the total change in the internal energy is also equal to zero (the right-hand side of the equation). Hence we can find the latent heat of sublimation of water at the triple point:
$v=\lambda +q=2.82\times {10}^{6}J/kg.$