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Chapter 8: Problem 66

Fish and wildlife managers have determined that a sudden temperature increase greater than \(5^{\circ} \mathrm{C}\) would be harmful to the marine ecosystem of a river. Warmer waters contain less dissolved oxygen and cause organisms in a river to increase their metabolism; if the temperature increase is sudden, the organisms do not have time to adapt to the new environment and likely will die. (Changes in river temperatures of five degrees and more due to seasonal temperature variations are common, but those temperature changes are gradual.) A proposed chemical plant plans to use river water for process cooling. The river flows at a rate of \(15.0 \mathrm{m}^{3} / \mathrm{s}\) at a temperature of \(15^{\circ} \mathrm{C}\), and a fraction of it will be diverted to the plant. Preliminary calculations reveal that the cooling water will remove \(5.00 \times 10^{5} \mathrm{kJ} / \mathrm{s}\) of heat from the plant. A portion of the extracted water will evaporate from the plant into the atmosphere, and the remainder will be returned to the river at a temperature of \(35^{\circ} \mathrm{C}\). (a) Draw and completely label a flowchart of the process and prove that there is enough information available to calculate all of the unknown stream flow rates on the chart. (b) Estimate the fraction of the river flow that must be diverted to the plant and the percentage of the cooling water that evaporates. Assume that water has a constant heat capacity of \(4.19 \mathrm{kJ} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)\) and a heat of vaporization roughly that of water at the normal boiling point, and also assume that the specific enthalpy of the water vapor relative to liquid water at \(15^{\circ} \mathrm{C}\) equals the heat of vaporization. (c) Write (but don't evaluate) an expression for the enthalpy change neglected by the assumption about the specific enthalpy of the steam.

Short Answer

Expert verified
Current data is enough to calculate unknown flow rates using an energy balance equation. The calculated percentage of evaporated water and fraction of river flow diverted to the plant will depend on the results of the balance equation. The expression for the neglected enthalpy change is represented by the difference of heat of vaporization and the product of final pressure, and the difference of saturated and initial steam pressure.

Step by step solution

01

Identifying Known and Unknown Values

Identify relevant values given in the problem, which include the flow rate of the river (\(15.0 \, \mathrm{m}^3 / \mathrm{s}\)), the initial water temperature (\(15^{\circ} \mathrm{C}\)), the heat removed by cooling (\(5.00 \times 10^{5} \, \mathrm{kJ} / \mathrm{s}\)), and the temperature of water after cooling (\(35^{\circ} \mathrm{C}\)). Calculate the initial enthalpy of the water using the given heat capacity.
02

Setting up the Energy Balance

The energy balance involves incoming and outgoing energy. Incoming energy includes the energy of the river flow, while outgoing energy includes the energy removed by the cooling system, energy associated with the evaporated water, and energy of water returned to the river.
03

Calculate the Unknown Flow Rates and Fraction of Water Diverted

One can use the energy balance equation, which states that incoming energy equals outgoing energy, to set up equations for deriving the flow rates and the fraction of water diverted for cooling. Solve these equations to get the desired results.
04

Calculate the Percentage of Water that Evaporates

By considering the energy associated with the evaporated water and the total energy removed by the cooling system, one can calculate the percentage of water that evaporates during the cooling process.
05

Write an Expression Neglected Enthalpy Change

The specific enthalpy of water vapor relative to liquid can be expressed as the heat of vaporization. Write an expression for the neglected enthalpy change in the water-steam transition, without actually calculating it. This can comprise the final pressure, initial pressure, and heat of vaporization.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Balance Calculation
Understanding energy balance calculations is essential for any aspiring chemical engineer. It's like piecing together a puzzle where energy entering and leaving a system must be accounted for. To put it simply, the energy that goes into a process plus or minus any changes within the system must equal the energy that comes out.

In the case of our river ecosystem, the process involves the heat absorbed by the river water used for cooling a plant, and the energy balance calculation ensures that the temperature increase does not exceed the critical threshold. By considering the flow rate of the river, the initial and final temperatures, and the heat removed, we can calculate the energy changes and maintain a safe environmental balance. This calculation becomes a safeguard for the ecosystem, preventing harm to marine life.
Enthalpy Change
Enthalpy change, in the world of chemistry and engineering, is akin to a fiscal report of a company 鈥� it measures the heat change during a process at constant pressure. Imagine a snapshot of your system鈥檚 'thermal revenue', providing insights into how much energy is absorbed or released.

In our river situation, calculating the enthalpy change helps quantify the heat absorbed from the river water by the plant and, subsequently, the heat released back into the river. By keeping track of this 'thermal transaction', engineers can estimate the change in energy content and ultimately ensure marine organisms' safety through controlled temperatures.
Mass and Energy Balances in Process Engineering
Picture mass and energy balances as the ledger books in process engineering. They are fundamental laws 鈥� akin to ensuring neither mass nor energy simply appear or disappear. Maintaining these balances is crucial for designing and operating any process system effectively and sustainably.

Applying these principles to our river and plant example, we ensure that all the mass taken in as cooling water can be accounted for as either evaporated water or water returned to the river. The energy taken from the plant as heat must also be accounted for in the temperature increase of the returned water or the latent heat of the evaporated water. These balances help engineers optimize processes, save costs, and preserve the environment by making informed, precise decisions.
Heat of Vaporization
Heat of vaporization is a measure of the warmth of the 'heartbreak' that occurs when a liquid says goodbye to its liquid state and transforms into vapor. It's the energy needed for this transformation at the boiling point under constant pressure. Every molecule must muster enough energy to break free from its liquid comrades and venture into the gaseous realm.

In the context of the plant using river water for cooling, some of this precious H2O is converted into vapor. This transition consumes energy 鈥� the heat of vaporization. By factoring in this value, engineers can determine how much water evaporates and thereby ensure the temperature of the water returned to the river doesn鈥檛 spell disaster for the local ecosystem.

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Most popular questions from this chapter

(a) Determine the specific enthalpy ( \(\mathrm{kJ} / \mathrm{mol}\) ) of \(n\) -pentane vapor at \(200^{\circ} \mathrm{C}\) and 2.0 atm relative to n-pentane liquid at \(20^{\circ} \mathrm{C}\) and \(1.0 \mathrm{atm}\), assuming ideal-gas behavior for the vapor. Show clearly the process path you construct for this calculation and give the enthalpy changes for each step. State where you used the ideal-gas assumption.

A natural gas containing 95 mole \(\%\) methane and the balance ethane is burned with \(20.0 \%\) excess air. The stack gas, which contains no unburned hydrocarbons or carbon monoxide, leaves the furnace at \(900^{\circ} \mathrm{C}\) and \(1.2 \mathrm{atm}\) and passes through a heat exchanger. The air on its way to the furnace also passes through the heat exchanger, entering it at \(20^{\circ} \mathrm{C}\) and leaving it at \(245^{\circ} \mathrm{C}\). (a) Taking as a basis \(100 \mathrm{mol} / \mathrm{s}\) of the natural gas fed to the furnace, calculate the required molar flow rate of air, the molar flow rate and composition of the stack gas, the required rate of heat transfer in the preheater, \(\dot{Q}\) (write an energy balance on the air), and the temperature at which the stack gas leaves the preheater (write an energy balance on the stack gas). Note: The problem statement does not give you the fuel feed temperature. Make a reasonable assumption, and state why your final results should be nearly independent of what you assume. (b) What would \(\dot{Q}\) be if the actual feed rate of the natural gas were 350 SCMH [standard cubic meters per hour, \(\left.\mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\right] ?\) Scale up the flowchart of Part (a) rather than repeating the entire calculation.

An aqueous slurry at \(30^{\circ} \mathrm{C}\) containing \(20.0 \mathrm{wt} \%\) solids is fed to an evaporator in which enough water is vaporized at 1 atm to produce a product slurry containing 35.0 wt\% solids. Heat is supplied to the evaporator by feeding saturated steam at 2.6 bar absolute into a coil immersed in the liquid. The steam condenses in the coil, and the slurry boils at the normal boiling point of pure water. The heat capacity of the solids may be taken to be half that of liquid water. (a) Calculate the required steam feed rate ( \(\mathrm{kg} / \mathrm{h}\) ) for a slurry feed rate of \(1.00 \times 10^{3} \mathrm{kg} / \mathrm{h}\). (b) Vapor recompression is often used in the operation of an evaporator. Suppose that the vapor (steam) generated in the evaporator described above is compressed to 2.6 bar and simultaneously heated to the saturation temperature at 2.6 bar, so that no condensation occurs. The compressed steam and additional saturated steam at 2.6 bar are then fed to the evaporator coil, in which isobaric condensation occurs. How much additional steam is required? (c) What more would you need to know to determine whether or not vapor recompression is economically advantageous in this process?

Among the best-known building blocks in nanotechnology applications are nanoparticles of noble metals. For example, colloidal suspensions of silver or gold nanoparticles (10-200 nm) exhibit vivid colors because of intense optical absorption in the visible spectrum, making them useful in colorimetric sensors. In the illustration shown below, a suspension of gold nanoparticles of a fairly uniform size in water exhibits peak absorption near a wavelength of \(525 \mathrm{nm}\) (near the blue region of the visible spectrum of light). When one views the solution in ambient (white) light, the solution appears wine-red because the blue part of the spectrum is largely absorbed. When the nanoparticles aggregate to form large particles, an optical absorption peak near \(600-700 \mathrm{nm}\) (near the red region of the visible spectrum) is observed. The breadth of the peak reflects a fairly broad particle size distribution. The solution appears bluish because the unabsorbed light reaching the eye is dominated by the short (blue-violet) wavelength region of the spectrum. since the optical properties of metallic nanoparticles are a strong function of their size, achieving a narrow particle size distribution is an important step in the development of nanoparticle applications. A promising way to do so is laser photolysis, in which a suspension of particles of several different sizes is irradiated with a high-intensity laser pulse. By carefully selecting the wavelength and energy of the pulse to match an absorption peak of one of the particle sizes (e.g., irradiating the red solution in the diagram with a \(525 \mathrm{nm}\) laser pulse), particles of or near that size can be selectively vaporized. (a) A spherical silver nanoparticle of diameter \(D\) at \(25^{\circ} \mathrm{C}\) is to be heated to its normal boiling point and vaporized with a pulsed laser. Considering the particle a closed system at constant pressure, write the energy balance for this process, look up the physical properties of silver that are required in the energy balance, and perform all the required substitutions and integrations to derive an expression for the energy \(Q_{\text {abs }}(\mathrm{J})\) that must be absorbed by the particle as a function of \(D(\mathrm{nm})\) (b) The total energy absorbed by a single particle \(\left(Q_{\text {abs }}\right)\) can also be calculated from the following relation: $$ Q_{\mathrm{abs}}=F A_{\mathrm{p}} \sigma_{\mathrm{abs}} $$ where \(F\left(\mathrm{J} / \mathrm{m}^{2}\right)\) is the energy in a single laser pulse per unit spot area (area of the laser beam) and \(A_{\mathrm{p}}\left(\mathrm{m}^{2}\right)\) is the total surface area of the nanoparticle. The effectiveness factor, \(\sigma_{\mathrm{ahs}},\) accounts for the efficiency of absorption by the nanoparticle at the wavelength of the laser pulse and is dependent on the particle size, shape, and material. For a spherical silver nanoparticle irradiated by a laser pulse with a peak wavelength of \(532 \mathrm{nm}\) and spot diameter of \(7 \mathrm{mm}\) with \(D\) ranging from 40 to \(200 \mathrm{nm}\), the following empirical equation can be used for \(\sigma_{\mathrm{abs}}\) $$ \sigma_{\mathrm{abs}}=\frac{1}{4}\left[0.05045+2.2876 \exp \left(-\left(\frac{D-137.6}{41.675}\right)^{2}\right)\right] $$ where \(\sigma_{\text {abs }}\) and the leading \(\frac{1}{4}\) are dimensionless and \(D\) has units of nm. Use the results of Part (a) to determine the minimum values of F required for complete vaporization of single nanoparticles with diameters of \(40.0 \mathrm{nm}, 80.0 \mathrm{nm},\) and \(120.0 \mathrm{nm}\). If the pulse frequency of the laser is \(10 \mathrm{Hz}\) (i.e., 10 pulses per second), what is the minimum laser power \(P(\mathrm{W})\) required for each of those values of D? (Hint: Set up a dimensional equation relating \(P\) to \(F\).) (c) Suppose you have a suspension of a mixture of \(D=40 \mathrm{nm}\) and \(D=120 \mathrm{nm}\) spherical silver nanoparticles and a \(10 \mathrm{Hz} / 532 \mathrm{nm}\) pulsed laser source with a \(7 \mathrm{nm}\) diameter spot and adjustable power. Describe how you would use the laser to produce a suspension of particles of only a single size and state what that size would be.

Propane is to be burned with \(25.0 \%\) excess air. Before entering the furnace, the air is preheated from \(32^{\circ} \mathrm{F}\) to \(575^{\circ} \mathrm{F}\) (a) At what rate (B tu/h) must heat be transferred to the air if the feed rate of propane is \(1.35 \times 10^{5}\) SCFH (ft \(^{3} / \mathrm{h}\) at \(\mathrm{STP}\) )? (b) The stack gas leaves the furnace at \(855^{\circ} \mathrm{F}\). How is the air likely to be preheated?
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