# Problem №2 (10 points)

In a vertical vessel with straight walls closed by a piston, there is water. Its height $h=2$ mm. There is no air in the vessel. To what height must the piston be raised so that all the water evaporates? The density of water $\rho=1000$ kg / $\mathrm{M}^{3}$, the molar mass of water vapor $M=0.018$ kg/mol, the pressure of saturated water vapor at a temperature $T=50{ }^{\circ} \mathrm{C}$ is $p=12300$ Pa. The temperature of the water and vapor is kept constant.
# Solution:

Mass of water in the vessel:

$m=\rho S h$, where $S-$ is the area of the base of the vessel.

(2 points)

Equation of state for an ideal gas for water vapor:

$p V=\frac{m}{M} R T$

where the volume occupied by the vapor $V=S(h+x)$.

(2 points)

As a result, we get:

$p S(h+x)=\frac{\rho S h}{M} R T$

(2 points)

## Final answer:

$$
x=\frac{\rho h R T}{M p}-h=\frac{1000 \cdot 0.002 \cdot 8.31 \cdot 323}{0.018 \cdot 12300}-0.002=24.2 \mu
$$