Discussion
For a non-magnetic metal, which one of the following graphs best represents the behaviour of \(\frac{C}{T}\) vs. \(T^{2}\), where \(C\) is the heat capacity and \(T\) is the temperature?
- A.
- B.
- C.
- D.
Answer: B
The plot is a straight line with a positive intercept, graph (B).
At low temperature the heat capacity of a non-magnetic metal is the sum of an electronic term, linear in \(T\), and the Debye phonon term, proportional to \(T^{3}\):
\[ \begin{aligned} C &= \gamma T + \beta T^{3} \\ \frac{C}{T} &= \gamma + \beta T^{2} \end{aligned} \]
Against \(T^{2}\) this is a straight line of slope \(\beta\) (from the phonons) cutting the axis at \(\gamma\) (from the conduction electrons). This is how the two contributions are separated experimentally.
A line through the origin (D) would describe an insulator with no electronic term. The two curved graphs do not follow from either term.
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