a. A sample of water vapor in an enclosed cylinder has an initial pressure of 500 Pa at an initial temperature of $-0.01^{\circ} \mathrm{C}$. A piston squeezes the sample smaller and smaller, without limit. Describe what happens to the water as the squeezing progresses. b. Repeat part a if the initial temperature is $0.03^{\circ} \mathrm{C}$ warmer

Solutions

VerifiedAs the piston squeezes the sample the pressure increases.

The initial pressure is less than $0.006 \mathrm{a}\mathrm{t}\mathrm{m}$.

In chapter 15 we defined 1atm as 101,300 Pa.

So $500\displaystyle $\mathrm{P}$$\mathrm{a}$\cdot$\frac{1atm}{101,300Pa}$=0.005 atm.

$ We now refer to the phase diagram in Figure 16.4.

**(a)**

In order to determine what will happen to a water vapor under these circumstances we need to take a look at a phase diagram for water (find it in the chapter).

The pressure of $500\mathrm{~Pa}$ is a bit less than 0.005 atm and the temperature of $-0.01\mathrm{^\circ C}$ is on the left side of the first vertical dashed line (at $0\mathrm{^\circ C}$). Therefore, the initial phase of water is gas, just as the problem tells us.