Chapter 22, Phase change Video Solutions, Thermodynamics: A complete undergraduate course

Problem 1

The gradient of the melting line of water on a $p-T$ diagram close to $0^{\circ} \mathrm{C}$ is $-1.4 \times 10^7 \mathrm{~Pa} / \mathrm{K}$. At $0^{\circ} \mathrm{C}$, the specific volume of water is $1.00 \times 10^{-3}$ $\mathrm{m}^3 \mathrm{~kg}^{-1}$ and of ice is $1.09 \times 10^{-3} \mathrm{~m}^3 \mathrm{~kg}^{-1}$. Using this information, deduce the latent heat of fusion of ice.

Manik Pulyani

Numerade Educator

03:02

Problem 2

Calculate the amount of energy required to convert $50 \mathrm{~g}$ of ice at $-10^{\circ} \mathrm{C}$ to steam at $150^{\circ} \mathrm{C}$. (The latent heats are $334 \mathrm{~kJ} / \mathrm{kg}$ and $2257 \mathrm{~kJ} / \mathrm{kg}$ for melting and vaporization, respectively. The heat capacities may be taken roughly constant at $2108 \mathrm{JK}^{-1} \mathrm{~kg}^{-1}, 4190 \mathrm{JK}^{-1} \mathrm{~kg}^{-1}, 2074 \mathrm{JK}^{-1} \mathrm{~kg}^{-1}$ for ice, water, steam).

Narayan Hari

Numerade Educator

08:59

Problem 3

Using the Clausius-Clapeyron equation, estimate the temperature at which water boils at the top of Mount Everest (altitude $8854 \mathrm{~m}$ ). (The air pressure is about $0.5 \mathrm{~atm}$ at a height of $18 \mathrm{~km}$.)

Shazia Naz

Numerade Educator

01:15

Problem 4

A pool of liquid in equilibrium with its vapour is converted totally into vapour in conditions of fixed temperature and pressure. What happens to the internal energy, the enthalpy, the Helmholtz function, and the Gibbs free energy?

David Collins

Numerade Educator

00:39

Problem 5

By how much can you lower the melting point of ice by pushing with your thumb on a drawing pin or thumb tack? (A thumb tack is a small metal pin with a large flat head; estimate the force you can apply and make a reasonable estimate of the area in contact with the ice at the sharp end.)

Averell Hause

Carnegie Mellon University

04:00

Problem 6

Find the depth of a glacier such that the bottom will melt in conditions where the atmospheric pressure is 1 atm and the temperature at the bottom of the glacier is $-5^{\circ} \mathrm{C}$.

Yaqub Khan

Numerade Educator

04:16

Problem 7

Consider the Clausius-Clapeyron equation applied to the liquid-vapour transition. Show that the second virial coefficient in the virial expansion for the gas affects $\mathrm{d} p / \mathrm{d} T$ in the opposite sense to the temperature dependence of the latent heat, so that the two effects tend to compensate one another. (The result is that (22.11) can sometimes be more accurate than (22.16)!)

Dr. Satish Ingale

Numerade Educator

02:37

Problem 8

It is quite common to see two of the coexistence lines at a triple point having almost the same gradient (i.e. the angle between them approaches $180^{\circ}$ ). What does this tell us about the properties of the three phases?

Nima Gharibi

Numerade Educator

01:57

Problem 9

Derivation of (22.12). Consider an arbitrary function of state $f$ expressed as a function of $p$ and $T$ (for a closed system): $\mathrm{d} f=\left.\frac{\partial f}{\partial T}\right|_p \mathrm{~d} T+$ $\left.\frac{\partial f}{\partial p}\right|_T \mathrm{~d} p$. Divide this expression by $\mathrm{d} T$ under the constraint that both $T$ and $p$ change but $\mathrm{d} p / \mathrm{d} T$ is fixed. Hence derive equation (22.12).

Dan Ni

Numerade Educator

02:44

Problem 10

Compare the Clausius-Clapeyron equation with the van 't Hoff equation.

Nicole Smina

Numerade Educator