 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 310

Summing over the $g$ internal states, the <number density>, <energy density>, and isotropic <pressure> are
$$
n=g\int\frac{d^3p}{(2\pi)^3}f(\mathbf p),
\qquad
\rho=g\int\frac{d^3p}{(2\pi)^3}E(\mathbf p)f(\mathbf p),
$$
and
$$
P=g\int\frac{d^3p}{(2\pi)^3}
\frac{\mathbf p^2}{3E(\mathbf p)}f(\mathbf p).
$$
The factor $\mathbf p^2/(3E)$ in the <kinetic pressure of an isotropic gas> is the angular average of one diagonal component of the momentum flux.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 1 / a / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 1 / a / ii / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 1 / a / ii / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)