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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

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

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:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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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
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

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