Speed of Sound
One mile above the surface of the Earth, the atmospheric air temperature is 0°C. If the ratio of specific heats is 1.5, what is the local speed of sound in m/s? Assume the molecular weight of air is 29 kg/kmol, and note the universal gas constant is 8,314 J/(kmol·K).
Expand Hint
The local speed of sound in an ideal gas is:
$$$c=\sqrt{kRT}$$$
where
$$k$$
is the ratio of specific heats,
$$R$$
is the specific gas constant, and
$$T$$
is the absolute temperature.
Hint 2
To find
$$R$$
:
$$$R=\frac{\bar{R}}{(mol.wt_i)}$$$
where
$$\bar R$$
is the universal gas constant.
To find the local speed of sound in an ideal gas:
$$$c=\sqrt{kRT}$$$
where
$$k$$
is the ratio of specific heats,
$$R$$
is the specific gas constant, and
$$T$$
is the absolute temperature. To find
$$R$$
:
$$$R=\frac{\bar{R}}{(mol.wt_i)}$$$
where
$$\bar R$$
is the universal gas constant. Thus,
$$$R=\frac{8,314J(kmol)}{(kmol\cdot K)(29kg)}=286.69\frac{J}{kg\cdot K}=286.69\:\frac{m^2}{s^2\cdot K}$$$
Finally, the local speed of sound in air is:
$$$c=\sqrt{(1.5)(286.69\frac{m^2}{s^2\cdot K})(0+273K)}=\sqrt{(430.035)(273)m^2/s^2}=342.6\:\frac{m}{s}$$$
342.6 m/s
Time Analysis
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