4. It is important to remember that the isentropic relations and normal shock relations are monotonic with Mach number and can be inverted. To illustrate this, consider the following problems, (a) Given a total temperature to static temperature ratio of 4, determine the Mach number. (b) If the entropy rises by ∆s/R = 1.0 across a shock, determine the pre- and post- shock Mach numbers and the static pressure jump (p2/p1).

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1 x 10 ° mm3 of air at a pressure of 10 bar and temperature 300°C, expands 10 times its original volume and its final temperature will be 25°C. Calculate (1) mass (ii) change in entropy by considering temperature, volume, entropy relationship (iii) change in entropy by considering temperature, pressure, entropy relationship (iii) change in entropy by considering pressure, volume, entropy relationship. Gas Molecular weight (M) (kJ/kg K) (kJ/kg K) Air 28.97 1.005 0.718 Oxygen Nitrogen Hydrogen Carbon monoxide 32 0.920 0.660 28 1.046 0.754 14.40 10.40 28 1.046 0.754