Question

Solid water (ice) is slowly warmed from a very low temperature. (a) What minimum external pressure p1 must be applied to the solid if a melting phase transition is to be observed? Describe the sequence of phase transitions that occur if the applied pressure pis such that$\mathit{p}\mathbf{<}{\mathit{p}}_{\mathbf{1}}$. (b) Above a certain

maximum pressure p, no boiling transition is observed. What is this pressure? Describe the sequence of phase transitions that occur if${\mathbf{p}}_{\mathbf{1}}\mathbf{<}\mathit{p}\mathbf{<}{\mathbf{p}}_{\mathbf{2}}$

Short answer

The pressure is 610 Pa and sublimation is occur if p < p1

The pressure is 221.2 X 105 Pa. and a transition from solid to liquid occur then second transition from liquid to vapour if p1 < p < p2

Step-by-step solution

About Solid water and triple point tempreature

Solid water—ice is frozen water. When water freezes, its molecules move farther apart, making ice less dense than water.This means that ice will be lighter than the same volume of water, and so ice will float in water.

The triple point of a substance is thetemperatureandpressureat which the threephases(gas,liquid, andsolid) of that substance coexist inthermodynamic equilibrium.

Determine the minimum external pressure applied to the solid to observe melting phase tansition 

First case:

As we given in the problem, there is a phase transition from Ice to liquid-

By back to phase diagram (figure ) we would find the pressure that responsible for melting the Ice is higher than the

pressure at triple point and by looking at table 18-3 we would find the pressure of water at the triple point equal 610 Pa

and this pressure cause the Ice starts to melt

the minimum pressure 131 that Would apply to observe the melting point is equal to the pressure at the triple point

The answer is

Second case:

Which phase transition occur if the applied pressure p is less than$p<p_1$

To answer this question we should back to ?gure i824 and we notice that before triple point where$p<p_1$, the phase transition which occur is sublimation, a transition from solid to vapour.

Second case:

Which phase transition occur if the applied pressure p is less than$p_2<p<p_1$

To anSWer this question We should back to figure and We notice that before triple point where $p<p_1$, the phase transition which occur is sublimation, a transition from solid to vapour.

Therefore the pressure is 610 Pa and sublimation is occur if $p<p_1$

;Determine the pressure above certain transition maximum pressure 

b _

First case:

In part (b) the problem tells us there is no boiling point transition observed and this means no phase transition occurred till

the critical point also, after the critical point, there is no phase change (review section 18.6 in the textbook)

By back to section 18.6 we Would find the pressure of water at the critical point equal

$222.12\times {10}^{5}Pa$

the maximum pressure p2 where no boiling transition occur is _$222.12\times {10}^{5}Pa$

Second case:

What is occur when$p_1<p<p_2$

By back to the phase diagram and look at the curves between the triple point p1 and the critical point p2 We Would find there are two phase transitions, first transition from solid to liquid then second transition from liquid to vapour. and this will

accurs if the applied pressure p is$p_1<p<p_2$

You can observe this at home occur to the ice converting to water then to vapour due to the applied pressure is the

atmospheric pressure where it is larger than$p_1$and less than $p_2$-

atmospheric pressure${10}^{5}Pa$

Therefore - 221.2 X 105 Pa. and a transition from solid to liquid occur then second transition from liquid to vapour if $p_1<p<p_2$