# Find the enthalpy change, internal energy change and entropy change across a shock wave.

Find the enthalpy change, internal energy change and entropy change across a shock wave whose upstream air temperature and pressure are $$300\,K$$ and $$1\,atm$$, and downstream air temperature and pressure are $$700\,K$$ and $$9\,atm$$.

Asked on 15th April 2021 in

Flow passing through a shock wave

Specific heat at constant pressure,
$c_{p}=\frac{\gamma R}{\gamma -1}=\frac{\left ( 1.4 \right )\left ( 287 \right )}{\left ( 1.4-1 \right )}=1004.5\,J/\left (kg.K \right )$
Specific heat at condtant volume,
$c_{v}=\frac{R}{\gamma -1}=\frac{287}{0.4}=717.5\,J/kg.K$
Enthalpy change across the shock wave,
$h_{2}-h_{1}=c_{p}\left ( T_{2}-T_{1} \right )=1004.5\left ( 700-300 \right )=4.018\times 10^{5}\,J/kg$
Internal energy change across the shock wave,
$e_{2}-e_{1}=c_{v}\left ( T_{2}-T_{1} \right )=717.5\left ( 700-300 \right )=2.87\times 10^{5}\,J/kg$
Entopy change across the shock wave,
$s_{2}-s_{1}=c_{p}ln\left ( \frac{T_{2}}{T_{1}} \right ) -Rln\left ( \frac{p_{2}}{p_{1}} \right ) =1004.5ln\left ( \frac{700}{300} \right )-287ln\left ( \frac{9}{1} \right )=220.51\,J/\left (kg.K \right )$