A) Explanation Given information: α V = 2.37 × 10 − 3 K − 1 κ T = 3.54 × 10 − 5 bar − 1 T 1 = 300 K P 1 = 1 bar V _ = 0 .100 L / mol Q = 5,000 kJ C P = 27 .5 J / mol ⋅ K The formula to calculate the coefficient of thermal expansion ( α V ) is given as follows: α V = 1 V _ ( ∂ V _ ∂ T ) P (1) Here, molar volume is V _ , and change in molar volume and change in temperature at constant pressure is ( ∂ V _ ) P , and ( ∂ T ) P respectively. Substitute 2.37 × 10 − 3 K − 1 for α V in equation (1). 1 V _ ( ∂ V _ ∂ T ) P = 2.37 × 10 − 3 K − 1 ( ∂ V _ ∂ T ) P = ( 2.37 × 10 − 3 K − 1 ) ( V _ ) The expression for the isothermal compressibility ( κ T ) is given as follows: κ T = − 1 V _ ( ∂ V _ ∂ P ) T (2) Here, change in molar volume and change in pressure at constant temperature is ( ∂ V _ ) T , and ( ∂ P ) T respectively. Substitute 3.54 × 10 − 5 bar − 1 for κ T in equation (2) − 1 V _ ( ∂ V _ ∂ P ) T = 3.54 × 10 − 5 bar − 1 The expression for the number of moles ( N ) in the system is given as follows. N = V V _ (3) Here, initial volume is V . Substitute 30 m 3 for V , and 0 .100 L / mol for V _ in equation (3). N = 30 m 3 0 .100 L / mol ( 1,000 L / m 3 ) = 30 m 3 0 .100 L / mol ( 1,000 L / m 3 ) = 300 , 000 mols Start with a closed system energy balance to find final temperature. U 2 − U 1 = Q + W E C d U = Q + ∫ P d V = Q + P ( V 2 − V 1 ) = Q − P ( V 1 − V 2 ) d U + P ( V 1 − V 2 ) = Q Q = d U + P d V (4) Here, final internal energy is U 2 , initial internal energy is U 1 , change in internal energy is d U , heat added or removed from the system is Q , compression work is W E C , pressure is P , and change in volume is d V . Since pressure is constant, write the equation for change in enthalpy ( d H ) . d H = d U + P d V (5) Here, internal energy is U . Substitute Q for d U + P d V in equation (5). d H = Q H 2 − H 1 = Q (6) Here, final enthalpy is H 2 , and initial enthalpy is H 1 . Since this is a constant P process, apply the constant pressure heat capacity in Equation (1) and rewrite the equation as, Q = ∫ N C P d T = N C P ( T 2 − T 1 ) (7) Here, constant pressure heat capacity is C P , final temperature is T 2 , and initial temperature is T 1 . Substitute 5,000 kJ for Q , 300 , 000 mols for N , 27 .5 J / mol ⋅ K for C P , and 300 K for T 1 in equation (7) B) Interpretation Introduction Interpretation: The final temperature and volume of the tank has to be determined when floating top is malfunction. Concept introduction: For the case of malfunction floating top, first use the energy balance for a constant volume system to find out the final temperature of the product. Then use the triple product relation between the partial derivative to the isothermal Compressibility, and the Coefficient of Thermal Expansion to obtain the final pressure of the tank.

The final temperature and volume of the tank has to be determined when floating top is working properly. Concept introduction: Initially calculate the number of moles in the system is calculated using the coefficient of thermal expansion and isothermal compressibility factor. Then use the energy balance equation to find out the final temperature of the tank.

Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

1st Edition

ISBN: 9781111580704

Author: Kevin D. Dahm, Donald P. Visco

Publisher: Cengage Learning

See similar textbooks

Question

Chapter 6.6, Problem 19P

Interpretation Introduction

Interpretation:

The final temperature and volume of the tank has to be determined when floating top is working properly.

Concept introduction:

Initially calculate the number of moles in the system is calculated using the coefficient of thermal expansion and isothermal compressibility factor. Then use the energy balance equation to find out the final temperature of the tank.

Interpretation Introduction

Interpretation:

The final temperature and volume of the tank has to be determined when floating top is malfunction.

Concept introduction:

For the case of malfunction floating top, first use the energy balance for a constant volume system to find out the final temperature of the product. Then use the triple product relation between the partial derivative to the isothermal Compressibility, and the Coefficient of Thermal Expansion to obtain the final pressure of the tank.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Chapter 6.6, Problem 18P

Chapter 6.6, Problem 20P

Knowledge Booster

Recommended textbooks for you

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
Elementary Principles of Chemical Processes, Bind...
Chemical Engineering
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Elements of Chemical Reaction Engineering (5th Ed...
Chemical Engineering
ISBN:9780133887518
Author:H. Scott Fogler
Publisher:Prentice Hall
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:9781119285915
Author:Seborg
Publisher:WILEY
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:9781285061238
Author:Lokensgard, Erik
Publisher:Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:9780072848236
Author:Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:McGraw-Hill Companies, The