 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

2021

Paper 1

An <adiabatic process> exchanges no heat with its surroundings, so $\delta Q=0$. For a reversible process it is also <entropy>[isentropic]. The first law then gives
$$
C_V\,dT=dE=-p\,dV.
$$
Using $p=Nk_BT/V$ and the Mayer relation,
$$
\frac{dT}{T}
=-\frac{Nk_B}{C_V}\frac{dV}{V}
=-(\gamma-1)\frac{dV}{V}.
$$
Integration yields
$$
TV^{\gamma-1}=\text{constant}.
$$
Substituting $T=pV/(Nk_B)$ gives the <reversible ideal-gas adiabat>
$$
\boxed{pV^\gamma=\text{constant}}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 36C / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 36C / c / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 36C / c / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)