Question

What is the relationship between temperature and mach number?

(a) T0=T\(\Big[1+\frac{\gamma-1}{2}M^2\Big]\)

(b) T0=T\(\Big[1+\frac{\gamma+1}{2}M^2\Big]\)

(c) T0=T\(\Big[1-\frac{\gamma-1}{2}M^2\Big]\)

(d) T0=T\(\Big[1-\frac{\gamma+1}{2}M^2\Big]\)

This question was posed to me by my school teacher while I was bunking the class.

I want to ask this question from Measurement of Mach Number in chapter Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Correct option is (a) T0=T\(\Big[1+\frac{\gamma-1}{2}M^2\Big]\)

The best explanation: The relationship between temperature and mach number is T0=T\(\Big[1+\frac{\gamma-1}{2}M^2\Big]\) where T is the temperature at that altitude, T_0 is the stagnation temperature, M is mach number and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.