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Introduction to Chemical Engineering Thermodynamics | 8th Edition | ISBN: 9781259696527 | Authors: J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart ISBN: 9781259696527 2049

Solution for problem 13.12 Chapter 13

Introduction to Chemical Engineering Thermodynamics | 8th Edition

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Introduction to Chemical Engineering Thermodynamics | 8th Edition | ISBN: 9781259696527 | Authors: J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart

Introduction to Chemical Engineering Thermodynamics | 8th Edition

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Problem 13.12

Humidity, relating to the quantity of moisture in atmospheric air, is accurately given by equations derived from the ideal-gas law and Raoult’s law for \(\mathrm{H}_{2} \mathrm{O}\).

(a) The absolute humidity h is defined as the mass of water vapor in a unit mass of dry air. Show that it is given by:

\(h=\frac{\mathscr{M}_{\mathrm{H}_{2} \mathrm{O}}}{\mathscr{M}_{\mathrm{air}}} \frac{p_{\mathrm{H}_{2} \mathrm{O}}}{P-p_{\mathrm{H}_{2} \mathrm{O}}}\)

where \(\mathscr{M}\) represents a molar mass and \(p_{\mathrm{H}_{2} \mathrm{O}}\) is the partial pressure of the water vapor, i.e., \(p_{\mathrm{H}_{2} \mathrm{O}}=y_{\mathrm{H}_{2} \mathrm{O}} P\).

(b) The saturation humidity \(h^{\mathrm{sat}}\) is defined as the value of h when air is in equilibrium with a large body of pure water. Show that it is given by:

\(h^{\mathrm{sat}}=\frac{\mathscr{M}_{\mathrm{H}_{2} \mathrm{O}}}{\mathscr{M}_{\mathrm{air}}} \frac{p_{\mathrm{H}_{2} \mathrm{O}}^{\mathrm{sat}}}{P-p_{\mathrm{H}_{2} \mathrm{O}}^{\mathrm{sat}}}\)

where \(p_{H_{2} O}^{\mathrm{sat}}\) is the vapor pressure of water at the ambient temperature.

(c) The percentage humidity is defined as the ratio of h to its saturation value, expressed as a percentage. On the other hand, the relative humidity is defined as the ratio of the partial pressure of water vapor in air to its vapor pressure, expressed as a percentage. What is the relation between these two quantities?

Text Transcription:

H_2O

h=M_H_2O/M_air p_H_2O/P-p_H_2O

M

p_H_2O

p_H_2O=y_H_2O P

h^sat

h^sat=M_H_2O/M_air p_H_2O^sat/P-p_H_2O^sat

p_H_2O^sat

Step-by-Step Solution:
Step 1 of 3

ENGR 103 Lecture 19 Resistance- the ability of an object to restrict or resist the flow of electrons in an electrical circuit - measured in ohms (Ω) Resistor- the circuit element responsible for restricting the flow of electrons - absorb energy from the electrons and dissipate it as heat - since there is a transfer of energy through a resistor, this means a difference in energy levels occur across the resistor constituting a voltage Ohms’s Law - Math: V = IR= 1 volt is equal to 1 ohm multiplied by the current (I) o Also one ohm= 1 volt divided by 1 Amp (I) - Passive sign convention must always be applied ; there for resistance is always positive - Circuit elements can be connected together in either a series or parallel way Series: elements in a series form a connection from end to end (like a train) - N number of Resistors in series can be combined to create a single equivalent resistance o Req Series= R1+R2+R3+…+RN - The current through each resistor is the Same o Iseries= I1=I2=I3=..,=IN - The total voltage drop across the equivalent resistance is equal to the sum of all individual resistor voltage drops o V series= V1+V2+V3…+VN Parallel Resistance= elements connect across each other like rungs of a ladder. - N number of resistors in parallel can be combined to create a single equivalent resistance o 1/ Req par. = 1/R1+1/R

Step 2 of 3

Chapter 13, Problem 13.12 is Solved
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Textbook: Introduction to Chemical Engineering Thermodynamics
Edition: 8
Author: J.M. Smith, Hendrick Van Ness, Michael Abbott, Mark Swihart
ISBN: 9781259696527

Introduction to Chemical Engineering Thermodynamics was written by Aimee Notetaker and is associated to the ISBN: 9781259696527. This full solution covers the following key subjects: . This expansive textbook survival guide covers 15 chapters, and 96 solutions. The answer to “?Humidity, relating to the quantity of moisture in atmospheric air, is accurately given by equations derived from the ideal-gas law and Raoult’s law for \(\mathrm{H}_{2} \mathrm{O}\).(a) The absolute humidity h is defined as the mass of water vapor in a unit mass of dry air. Show that it is given by:\(h=\frac{\mathscr{M}_{\mathrm{H}_{2} \mathrm{O}}}{\mathscr{M}_{\mathrm{air}}} \frac{p_{\mathrm{H}_{2} \mathrm{O}}}{P-p_{\mathrm{H}_{2} \mathrm{O}}}\)where \(\mathscr{M}\) represents a molar mass and \(p_{\mathrm{H}_{2} \mathrm{O}}\) is the partial pressure of the water vapor, i.e., \(p_{\mathrm{H}_{2} \mathrm{O}}=y_{\mathrm{H}_{2} \mathrm{O}} P\).(b) The saturation humidity \(h^{\mathrm{sat}}\) is defined as the value of h when air is in equilibrium with a large body of pure water. Show that it is given by:\(h^{\mathrm{sat}}=\frac{\mathscr{M}_{\mathrm{H}_{2} \mathrm{O}}}{\mathscr{M}_{\mathrm{air}}} \frac{p_{\mathrm{H}_{2} \mathrm{O}}^{\mathrm{sat}}}{P-p_{\mathrm{H}_{2} \mathrm{O}}^{\mathrm{sat}}}\)where \(p_{H_{2} O}^{\mathrm{sat}}\) is the vapor pressure of water at the ambient temperature.(c) The percentage humidity is defined as the ratio of h to its saturation value, expressed as a percentage. On the other hand, the relative humidity is defined as the ratio of the partial pressure of water vapor in air to its vapor pressure, expressed as a percentage. What is the relation between these two quantities?Text Transcription:H_2Oh=M_H_2O/M_air p_H_2O/P-p_H_2OMp_H_2Op_H_2O=y_H_2O Ph^sath^sat=M_H_2O/M_air p_H_2O^sat/P-p_H_2O^satp_H_2O^sat” is broken down into a number of easy to follow steps, and 180 words. The full step-by-step solution to problem: 13.12 from chapter: 13 was answered by Aimee Notetaker, our top Engineering and Tech solution expert on 06/03/22, 04:28PM. Since the solution to 13.12 from 13 chapter was answered, more than 201 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Introduction to Chemical Engineering Thermodynamics, edition: 8.

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