Physics For Scientists And Engineers
Physics For Scientists And Engineers
6th Edition
ISBN: 9781429201247
Author: Paul A. Tipler, Gene Mosca
Publisher: W. H. Freeman
Question
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Chapter 38, Problem 32P

(a)

To determine

Proof of P=25NEFV=CV5/3 .

(a)

Expert Solution
Check Mark

Answer to Problem 32P

The proof of P=25NEFV=CV5/3 has been determined.

Explanation of Solution

Given:

The monatomic ideal-gas relation is,

  PV=23NEav   ..... (1)

The Fermi energy from equation 38-22b is,

  EF=(0.3646eVnm2)(NV)2/3 …... (2)

The average energy from equation 38-23 is,

  Eav=35EF   ..... (3)

Calculation:

From equation (1) and (3),

  PV=23N(35EF)PV=25NEFP=25NEFV   ..... (4)

From equation (4) and (2),

  P=25NV(0.3646eV nm2)( N V)2/3=(0.3646eV nm2)25( N V)5/3=(0.3646eV nm2)25N5/3V5/3=CV5/3   ..... (5)

Hence, equation P=25NEFV=CV5/3 is proved.

Conclusion:

Therefore, the proof of P=25NEFV=CV5/3 has been determined.

(b)

To determine

Proof of B=53P=23NEFV .

(b)

Expert Solution
Check Mark

Answer to Problem 32P

The proof of B=53P=23NEFV has been determined.

Explanation of Solution

Given:

The expression of bulk modulus is,

  B=VPV   ..... (6)

From equation (5) and (6),

  B=V( C V 5/3 )V=V(53CV 8/3)=53CV5/3=53P(P=CV 5/3 )

Substitute value of P from equation (4) in above equation,

  B=53(25 N E F V)=23NEFV   ..... (7)

Conclusion:

Therefore, the proof of B=53P=23NEFV has been determined.

(c)

To determine

The bulk modulus for copper.

(c)

Expert Solution
Check Mark

Answer to Problem 32P

The bulk modulus for copper is 63.6×109N/m2 .

Explanation of Solution

Given:

The value of N/V for Copper from Table 38-1 is N/V=84.7electrons/nm3

The Fermi energy for copper from Table 38-1 is EF=7.03eV

Calculation:

From equation (7), the bulk modulus for copper is calculated as,

  B=23(84.7electrons/ nm 3)(7.03eV)=23(84.7× 10 27electrons/ m 3)(7.03eV)( 1.602× 10 19 Nm 1eV)=63.593×109N/m263.6×109N/m2

Comparison of 63.6×109N/m2 with 140×109N/m2 is,

  140×109N/m263.6×109N/m2=2.2

Conclusion:

Therefore, the bulk modulus for copper is 63.6×109N/m2 .

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