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Chapter 7: Q. 7.58 (page 313)

The speed of sound in copper is 3560m/s. Use this value to calculate its theoretical Debye temperature. Then determine the experimental Debye temperature from Figure 7.28, and compare.

Short Answer

Expert verified

Hence, the Debye Temperature from experimental Data (graph) TD=359.9176K.

Step by step solution

01

Step 1. Given information

We have,the speed of sound in copper is3560m/s

The Debye temperature isTD=hCs2kB·6NπV13.


02

Step 2. Putting the value of h , V , N ,CS ,kB.

V=7.11cm3/mol

Cs=3560m/s=3560×100cm/s

N=6.022×1023atoms/mol

kB=1.381×10-23J/K

h=6.626×10-34J·s

substituting all the above value in Debye Temperature we get

TD=6.626×10-34J·s×3560×100cm/s2×1.381×10-23J/K6×6.022×1023/molπ×7.11cm3/mol13

∴TD=465.3381K

03

Step 3.  Calculating the experimental Debye Temperature.

Take any two points on experimental data calculate the slope [Approximately] Approximately take two points

Approximately take two points

A(0,0.75)B(18,1.5)

ΔCVTΔT2=1.5-0.7518-0

=0.0417

04

Step 4. Finding the slope of the graph.

Slope:ΔCVTΔT2=12π4NkB5TD3

12π4NkB5TD3=0.0417mJ/K4

then , the Debye Temperature

TD=12π4NkB5×0.0417×10-3J/K413

=12π4×6.022×1023×1.381×10-235×0.0417×10-313

=359.9176K

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