Isothermal shock
= Isothermal shock
{title2=$\rho_2/\rho_1=\mathcal M_1^2$}
An isothermal shock joins two states at the same <temperature> and <isothermal sound speed>. Mass and <momentum> conservation imply $u_1u_2=c_s^2$ for a nontrivial planar jump, so the compression ratio is the upstream isothermal Mach number squared. <Heat> exchange replaces adiabatic energy conservation across the gas alone.