Question

Fermi temperature when number density increased to eight times

Answer 1

Answer on Question #71454, Physics / Molecular Physics | Thermodynamics

Fermi temperature when number density increased to eight times

Solution:

Fermi temperature by definition

$$T _ {F} = \frac {\hbar^ {2}}{2 m k _ {B}} (3 \pi^ {2} n) ^ {2 / 3}$$

Thus

$$T _ {F} \sim n ^ {2 / 3}$$

When the number density increased to eight times

$$T _ {F} \sim (8 n) ^ {2 / 3} = 4 n ^ {2 / 3} = 4 T _ {F 0}$$

**Answer:** Fermi temperature increased to four times.

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