Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
Bartleby Related Questions Icon

Related questions

Question

A liquid has a molar volume of 0.2 L/mol at 400 K and 4 bar. This liquid is compressed with a pump that operates at steady-state and adiabatically. The liquid enters the pump at a rate of 3 mol/s, at a temperature of 400 K and pressureof 4 bar and exits at a pressure of 20 bar.

The liquid has the following properties which can be used (if needed) in the solution:
• Coefficient of thermal expansion, αV = 2 x 10-3 K-1
• Isothermal compressibility factor, κT = 4 x 10-5 bar-1
• Cp = Cv = 30 J/mol-K

Find the following:
A) Work done by the pump
B) Temperature of the liquid leaving the pump
C) Molar volume of the liquid leaving the pump

Expert Solution
Check Mark
Step 1: First Step:-

A. Work done by the pump

The work done by the pump is given by the following formula:

  • W equals n R T left parenthesis 1 minus 1 divided by kappa T left parenthesis P 2 divided by P 1 right parenthesis right parenthesis

where

  • n is the number of moles of liquid entering the pump per unit time (3 m o l divided by s)
  • R is the universal gas constant (8.314 space J divided by m o l minus K)
  • T is the temperature of the liquid entering the pump (400 K)
  • P1 is the pressure of the liquid entering the pump (4 b a r)
  • P2 is the pressure of the liquid leaving the pump (20 b a r)
  • κT is the isothermal compressibility factor of the liquid (4 space x 10 minus 5 space b a r minus 1)

Substituting the given values, we get the work done by the pump as follows:

  • W equals left parenthesis 3 m o l divided by s right parenthesis left parenthesis 8.314 space J divided by m o l minus K right parenthesis left parenthesis 400 space K right parenthesis left parenthesis 1 minus 1 divided by left parenthesis 4 space x space 10 minus 5 space b a r minus 1 right parenthesis left parenthesis 20 space b a r divided by 4 space b a r right parenthesis right parenthesis equals 1263 J divided by s

B. Temperature of the liquid leaving the pump

The temperature of the liquid leaving the pump can be found using the following formula:

  • T 2 equals T 1 left parenthesis P 1 divided by P 2 right parenthesis to the power of 2 space end exponent left parenthesis 1 minus y right parenthesis

where

  • T1 is the temperature of the liquid entering the pump (400 k)
  • P1 is the pressure of the liquid entering the pump (4 b a r)
  • P2 is the pressure of the liquid leaving the pump (20 b a r)
  • γ is the adiabatic index of the liquid (1.4)

Substituting the given values, we get the temperature of the liquid leaving the pump as follows:

  • T 2 equals 400 K left parenthesis 4 b a r divided by 20 b a r right parenthesis squared left parenthesis 1 minus 1.4 right parenthesis equals 280 K

Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Introduction to Chemical Engineering Thermodynami...
Chemical Engineering
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:McGraw-Hill Education
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemical Engineering
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Text book image
Elements of Chemical Reaction Engineering (5th Ed...
Chemical Engineering
ISBN:9780133887518
Author:H. Scott Fogler
Publisher:Prentice Hall
Text book image
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:9781119285915
Author:Seborg
Publisher:WILEY
Text book image
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:9781285061238
Author:Lokensgard, Erik
Publisher:Delmar Cengage Learning
Text book image
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:9780072848236
Author:Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:McGraw-Hill Companies, The