Past exam of the physics B course of the University of Cambridge / 2010 / Paper 2B / Section A

The reversible isothermal ideal-gas work is $Q=R{T}_0\ln 2$; the heat would not be fixed by endpoints alone without the process assumption.

Full derivation: solution.

Pairing adjacent contributions from the Biot-Savart law gives magnitude ${\mu }_{0}IN(N+1)/(4\pi a)$, directed opposite to the first wire's field at the observation point.

Full derivation: solution.

The lowest transverse electric mode has cutoff frequency $c/(2a)\simeq 15.0\mathrm{GHz}$; propagation requires frequency strictly above cutoff.

Full derivation: solution.

Two distinct reversible adiabats would form a one-reservoir cycle with an isotherm, contradicting the Kelvin-Planck statement of the second law.

Full derivation: solution.

The trihydrogen cation has one breathing normal mode and two degenerate in-plane distortion normal modes. Rigid translations and rotations do not count as vibrations.

Full derivation: solution.