Answer:
The Debye temperature for aluminum is 375.2361 K
Explanation:
Molecular weight of aluminum=26.98 g/mol
T=15 K
The mathematical equation for the specific heat and the absolute temperature is:
[tex]C_{v} =AT^{3}[/tex]
Substituting in the expression of the question:
[tex]C_{v} =(\frac{12\pi ^{4}R }{5\theta _{D}^{3} } )T^{3}[/tex]
[tex]\theta _{D} =(\frac{12\pi ^{4}RT^{3} }{5C_{v} } ) ^{1/3}[/tex]
Here
[tex]C_{v} =4.6\frac{J}{kg-K} *\frac{1kg}{1000g} *\frac{26.98g}{1mol} =0.1241J/mol-K[/tex]
Replacing:
[tex]\theta _{D} =(\frac{12\pi ^{4}*8.31*15^{3} }{5*0.1241} )^{1/3} =375.2361K[/tex]
