Question

What is the relation between speed of object and temperature?

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

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

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

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

This question was posed to me during an interview.

Question is taken from Measurement of Air Temperature in chapter Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

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

To elaborate: The relation between speed of object and temperature is T0=T\(\Big[1+\frac{\gamma-1}{2}(\frac{V}{a})^2\Big]\)  where T is the temperature at that altitude, T0 is the stagnation temperature, γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume, V is speed of object and ‘a’ is speed of sound.