How many phase rule variables must be specified to fix the thermodynamic state of each of the following systems? (a) A sealed flask containing a liquid ethanol-water mixture in equilibrium with its vapor. (b) A sealed flask containing a liquid ethanol-water mixture in equilibrium with its vapor and nitrogen. (c) A sealed flask containing ethanol, toluene, and water as two liquid phases plus vapor.

Various species of hagfish, or slime eels, live on the ocean floor, where they burrow inside other fish, eating them from the inside out and secreting copious amounts of slime. Their skins are widely used to make eelskin wallets and accessories. Suppose a hagfish is caught in a trap at a depth of 200 m below the ocean surface, where the water temperature is $10^\circ C,$ then brought to the surface where the temperature is $15^\circ C.$ If the isothermal compressibility and volume expansivity are assumed constant and equal to the values for water, $\left(\beta=10^{-4} \mathrm{K}^{-1} \text { and } \kappa=4.8 \times 10^{-5} \mathrm{bar}^{-1}\right)$ what is the fractional change in the volume of the hagfish when it is brought to the surface?

Identify the center of each power series. Then write the first five terms of the power series. $\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n}}{(n-1) !}$

Liquid-liquid two-phase coexistence in pure (that is, one-component) systems is extremely rare. Using library and Internet resources, find two examples of liquid-liquid coexistence in a pure material.

Underline each prepositional phrase and circle each appositive phrase. Brad looked under the hood to see what was wrong with the car.

Insert a colon where necessary. If the sentence is correct, write C in the blank. _____ I have to get up early tomorrow to catch the 7:00 A.M. bus.

A system comprised of chloroform, 1,4-dioxane, and ethanol exists as a two-phase vapor/liquid system at $50^\circ C$ and 55 kPa. After the addition of some pure ethanol, the system can be returned to two-phase equilibrium at the initial T and P. In what respect has the system changed, and in what respect has it not changed?

A closed, nonreactive system contains species 1 and 2 in vapor/liquid equilibrium. Species 2 is a very light gas, essentially insoluble in the liquid phase. The vapor phase contains both species 1 and 2. Some additional moles of species 2 are added to the system, which is then restored to its initial T and P. As a result of the process, does the total number of moles of liquid increase, decrease, or remain unchanged?

An instrument to measure the acceleration of gravity on Mars is constructed of a spring from which is suspended a mass of 0.40 kg. At a place on earth where the local acceleration of gravity is $9.81 m \cdot s^{−2},$ the spring extends 1.08 cm. When the instrument package is landed on Mars, it radios the information that the spring is extended 0.40 cm. What is the Martian acceleration of gravity?

The specific volume of isobutane liquid at 300 K and 4 bar is $1.824 \mathrm{cm}^{3} \cdot \mathrm{g}^{-1}.$ Estimate the specific volume at 415 K and 75 bar.

At what absolute temperature do the Celsius and Fahrenheit temperature scales give the same numerical value? What is the value?

The Tait equation for liquids is written for an isotherm as: $V=V_{0}\left(1-\frac{A P}{B+P}\right)$ where V is molar or specific volume, $V_0$ is the hypothetical molar or specific volume at zero pressure, and A and B are positive constants. Find an expression for the isothermal compressibility consistent with this equation.

Liquid water at $180^{\circ} \mathrm{C}$ and 1002.7 kPa has an internal energy (on an arbitrary scale) of $762.0 \mathrm{kJ} \cdot \mathrm{kg}^{-1}$ and a specific volume of $1.128 \mathrm{cm}^{3} \cdot \mathrm{g}^{-1}.$ (a) What is its enthalpy? (b) The water is brought to the vapor state at $300^{\circ} \mathrm{C}$ and 1500 kPa, where its internal energy is $2784.4 \mathrm{kJ} \cdot \mathrm{kg}^{-1}$ and its specific volume is $169.7 \mathrm{cm}^{3} \cdot \mathrm{g}^{-1}.$ Calculate $\Delta U$ and $\Delta H$ for the process.

The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90 percent. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa (absolute), respectively, determine the mechanical efficiency of the pump. Answer: 74.1 percent