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
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Chapter 11, Problem 11.16P
Interpretation Introduction

Interpretation:

To show lim n0ΔH˜=0

Expert Solution
Check Mark

Explanation of Solution

Given Information:

  ΔH= x1+x2(A21x1+A12x2)

ΔH for particular solute (1)/solute (2) is represented by the equation:

  ΔH= x1+x2(A21x1+A12x2)..... (A)

Rewrite the equation (A) using the definition of n˜ and ΔH

x1=11+n˜ΔH=ΔH(1+n˜)x2=1x1x2=n˜1+n˜

Now the equation (A) will become

  ΔH= n˜1+ n˜(A211+n˜+A12n˜1+n˜).........(1)

Now show that, lim n0ΔH˜=0

Thus, Equation 1 will

become,

  lim n0ΔH˜=lim n0(  n ˜1+  n ˜( A 21 1+ n ˜ + A 12 n ˜ 1+ n ˜ ))              =  01+ 0( A 211+0+ A 1201+0)lim n0ΔH˜=0

Hence, lim n0ΔH˜=0

Interpretation Introduction

Interpretation:

To show lim nΔH˜=A12

Expert Solution
Check Mark

Explanation of Solution

Given Information:

  ΔH= x1+x2(A21x1+A12x2)

ΔH for particular solute (1)/solute (2) is represented by the equation:

  ΔH= x1+x2(A21x1+A12x2)..... (A)

Rewrite the equation (A) using the definition of n˜ and ΔH

x1=11+n˜ΔH=ΔH(1+n˜)x2=1x1x2=n˜1+n˜

Now the equation (A) will become

  ΔH= n˜1+ n˜(A211+n˜+A12n˜1+n˜).........(1)

Now show that, lim nΔH˜=A12

As n,n˜1+n˜1

Thus, Equation 1 will

become,

  lim n˜ΔH˜=lim n˜(  n ˜1+  n ˜( A 21 1+ n ˜ + A 12 n ˜ 1+ n ˜ ))              = 1(0+A12)lim n˜ΔH˜=A12

Hence, lim n˜ΔH˜=A12

Interpretation Introduction

Interpretation:

To show lim n˜0dΔH˜/dn˜=A21

Expert Solution
Check Mark

Explanation of Solution

Given Information:

  ΔH= x1+x2(A21x1+A12x2)

Show that, lim n˜0dΔH˜/dn˜=A21

As we know that

dΔH/dn˜=H˜2E

Thus,

  lim n˜˜0H˜2E=A21

Here, H˜2E is defined as H˜2E=x12[A21+2(A21+2(A12A21)x2)]

Now,

substituting x1and x2expression in terms of n˜ in the above equation.

  H˜2E=(1 1+ n ˜ )2[A21+2(A 21+2(A 12A 21) n ˜ 1+ n ˜ )]n˜0lim H ˜2En˜=limn˜0(( 1 1+ n ˜ )2[A 21+2( A 21 +2( A 12 A 21 ) n˜ 1+n˜ )])           =12(( A 21)+2( A 12 A 21)0)lim H ˜2En˜=A21lim n˜0dΔH˜/dn˜=A21

Hence, lim n˜0dΔH˜/dn˜=A21

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