Problems about thermodynamics – equations need help for the following problems.

1.17 (Virial and Van-der-Waal’s equation of state) – seperate file as hints is attached

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Problems about thermodynamics – equations need help for the following problems.
1.17 (Virial and Van-der-Waal’s equation of state) – seperate file as hint

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1.33 (3-step cyclic process)

1.51 (Combustion of glucose)

1.54 (Climbing Mount Ogden)

2.25 (Random Walk)

2.29 (The Entropy of 2 Einstein solids.) Check the hints for 1.17 (attached) as a second file

For problem 1.51; the reference table is attracted at the end of this file

Do not solve problem 2.24, I need help for the solution of problem 2.25

Below is the section 1.17 mentioned in the problem 2.25 section (c)

Reference table for problem 1.51

Question 1.17

The Van-der-Waals equation of state is

an2

P + 2 (V ? nb) = nRT

V

Pulling the factor of V out of the second set of parentheses,

an2

nb

P + 2 V 1?

= nRT

V

V

(1)

(2)

and divide both sides by (1 ? nb/V )

an2

nb ?1

P + 2 V = nRT 1 ?

V

V

(3)

Then we use the binomial expansion given in the book on the term on the RHS (1 ? nb/V )?1 . Ill do

the first two terms:

(1 + x)p ? 1 + px + . . .

(4)

Looking at what weve got, x = ?nb/V and p = -1, and so

nb

nb ?1

?1+

+ …

1?

V

V

(5)

Inserting this into equation (3):

an2

nb

P + 2 V = nRT 1 +

+ …

V

V

b

= nRT 1 +

+ …

(V /n)

(6)

Moving the second term on the left hand side over to the right hand side gives us:

an2

P V = nRT 1 +

+ … ?

V

(a/RT )n

= nRT 1 +

+ . . . ? nRT

V

(a/RT )

= nRT 1 +

+ . . . ? nRT

(V /n)

(a/RT )

= nRT 1 +

?

+ …

(V /n)

1

= nRT 1 + (b ? a/RT )

+ …

(V /n)

b

(V /n)

b

(V /n)

b

(V /n)

b

(V /n)

1

(7)

Comparing this to the Virial equation of state:

B(T )

C(T )

P V = nRT 1 +

+

+ …

(V /n) (V /n)2

(8)

we can see by comparing the two equations, and looking at the term proportion to

1

(V /n) ,

B(T ) = b ? (a/RT )

To get C(T ) you need to include the next term in the binomial expansion (the

1

which will result in a term proportional to (V /n)

2.

2

that

(9)

1

2 p(p

? 1)x2 term),

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