Question

Which of the following is the correct isentropic relation between pressure and temperature?

(a) \(\frac{p_1}{p_2}=(\frac{T_2}{T_1})^\frac{\gamma}{1-\gamma}\)

(b) \(\frac{p_1}{p_2}=(\frac{T_2}{T_1})^\frac{\gamma-1}{\gamma}\)

(c) \(\frac{p_1}{p_2}=(\frac{T_2}{T_1})^\frac{\gamma+1}{\gamma}\)

(d) \(\frac{p_1}{p_2}=(\frac{T_2}{T_1})^\frac{\gamma}{\gamma-1}\)

I got this question in unit test.

I'm obligated to ask this question of Measurement of Airspeed topic in division Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Right option is (a) \(\frac{p_1}{p_2}=(\frac{T_2}{T_1})^\frac{\gamma}{1-\gamma}\)

Explanation: \(\frac{p_1}{p_2}=(\frac{T_2}{T_1})^\frac{\gamma}{1-\gamma}\)   is the correct isentropic relation between pressure and temperature where p1, p2 are pressures, T1, T2 are temperatures and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.