Question

At what temperature is the speed of sound in methane, CH4 equal to the speed of sound in air at room temperature?

Answer 1

Expression for the speed of sound in methane:

$$u=\sqrt{\frac{\gamma_1 RT_1}{\Mu_1}}$$

The same speed of sound is in air (assuming that room temperature is 300 K):

$$u=\sqrt{\frac{\gamma_2 RT_2}{\Mu_2}}$$

Equate and solve for temperature of methane:

$$\sqrt{\frac{\gamma_1 RT_1}{\Mu_1}}=\sqrt{\frac{\gamma_2 RT_2}{\Mu_2}},\\\space\\ T_1=T_2\frac{\Mu_1\gamma_2}{\Mu_2\gamma_1},\\\space\\ T_1=300\cdot\frac{16\cdot1.398}{29\cdot1.410}=183\text{ K},$$

or -90.15°