# Find the upstream Mach number if there is a entropy increase across the normal shock wave of \(220\,J/\left( {kg.K} \right)\).

Find the upstream Mach number if there is an entropy increase across the normal shock wave of \(220\,J/\left( {kg.K} \right)\).

Entropy is a measure of molecular disorder or randomness in any system. Useful work is obtained when there is a ordered molecular motion, so entropy of a system is the measure of thermal energy per unit temperature which is unavailable for doing any useful work. Entropy change across a normal shock is given by

\[\frac{{{p_{02}}}}{{{p_{01}}}} = {e^{ – \left( {{s_2} – {s_1}} \right)/R}}\]

\[ \Rightarrow \frac{{{p_{02}}}}{{{p_{01}}}} = {e^{ – \left( {220} \right)/287}} = 0.46\]

Therefore, from normal shock properties table, for, \(\frac{{{p_{02}}}}{{{p_{01}}}} = 0.46\), upstream Mach number \(M_1\), is around \(2.6\).