Question 1.45: It is of interest to compare the sonic velocity for air, car...

The sonic velocities for the three common gases at 45^{\circ } C are computed by applying Equation 1.162 C=\sqrt{\frac{E_{\upsilon }}{\rho } } =\sqrt{\frac{k_{p}}{\rho } } =\sqrt{\frac{k_{p}RT }{\rho } } =\sqrt{kRT} as follows:
C=\sqrt{kRT}
where the values for k and R, which are each independent of both the pressure and the temperature of the gas, are read from Table A.5 in Appendix A.
(a) The sonic velocity for air at 45^{\circ } C is determined as follows:

N:=kg\frac{m}{sec^{2} }               T:=45^{\circ } C=318.15K
k_{air}: =1.4              R_{air}: =287\frac{Nm}{kgK}               C_{air}: =\sqrt{k_{air}R_{air}T} =357.537\frac{m}{s}

(b) The sonic velocity for helium at 45^{\circ } C is determined as follows:

k_{He} :=1.4               R_{He}:=2077\frac{Nm}{kgK}                C_{He}: =\sqrt{k_{He}R_{He}T} =1.047\times 10^{3} \frac{m}{s}
\frac{C_{He}}{C_{air}} =2.929

Thus, the sonic velocity of helium is about three times the sonic velocity of air, both at a temperature of 45^{\circ } C.
(c) The sonic velocity for hydrogen at 45^{\circ } Cis determined as follows:

k_{H2} :=1.4               R_{H2}:=4120\frac{Nm}{kgK}                C_{H2}: =\sqrt{k_{H2}R_{H2}T} =1.355\times 10^{3} \frac{m}{s}
\frac{C_{H2}}{C_{air}} =3.789               \frac{C_{H2}}{C_{He}} =1.293

Thus, the sonic velocity of hydrogen is almost four times the sonic velocity of air, and about 1.3 times the sonic velocity of helium, all at a temperature of 45^{\circ } C.