Answer to Question #102251 in Classical Mechanics for BIVEK

Question

The molar heat capacity of Titanium at 25ºC is 26.06 J /mol/K

. Estimate its
Debye temperature.

Answer 1

The molar heat capacity can be expressed in terms of Debye temperature:

$$C_\mu=\bigg(\frac{12}{5}\bigg)\pi^4R\bigg(\frac{T}{\Theta}\bigg)^3,\\ \space\\ \Theta=T\sqrt[3]{\frac{12\pi^4R}{5C_\mu}}=\\=(25+273)\sqrt[3]{\frac{12\cdot3.14^4\cdot8.314}{5\cdot26.06}}=1254\text{ K}.$$