Question #2272

The highest natural atmospheric temperature ever recorded on Earth was 58°C (136°F), at El Azizia, Libya on September 13, 1922. The record low temperature was −89°C (−129°F), which occurred at the Soviet Vostok Station in Antarctica on July 21, 1983. What is the difference in the speed of sound in air for these two extreme temperatures? answer in m/s.

Expert's answer

The speed of sound in the dry air can be derived by the formula:

<img src="/cgi-bin/mimetex.cgi?c_%7B%5Cmathrm%7Bair%7D%7D%20=%20331.3%20%5Cmathrm%7Bm%20%5Ccdot%20s%5E%7B-1%7D%7D%20%5Csqrt%7B1+%5Cfrac%7BT%7D%7B273.15%5C;%5E%7B%5Ccirc%7D%5Cmathrm%7BC%7D%7D%7D" title="c_{\mathrm{air}} = 331.3 \mathrm{m \cdot s^{-1}} \sqrt{1+\frac{T}{273.15\;^{\circ}\mathrm{C}}}">

Thus at T = 58°C:

<img src="http://latex.codecogs.com/gif.latex?c_%7B%5Cmathrm%7Bair%7D%7D%20=%20331.3%20%5Cmathrm%7Bm%20%5Ccdot%20s%5E%7B-1%7D%7D%20%5Csqrt%7B1+%5Cfrac%7B58%7D%7B273.15%5C;%5E%7B%5Ccirc%7D%5Cmathrm%7BC%7D%7D%7D%20=%20364.78" title="c_{\mathrm{air}} = 331.3 \mathrm{m \cdot s^{-1}} \sqrt{1+\frac{58}{273.15\;^{\circ}\mathrm{C}}} = 364.78">

At T = -89°C:

<img src="http://latex.codecogs.com/gif.latex?c_%7B%5Cmathrm%7Bair%7D%7D%20=%20331.3%20%5Cmathrm%7Bm%20%5Ccdot%20s%5E%7B-1%7D%7D%20%5Csqrt%7B1+%5Cfrac%7B-89%7D%7B273.15%5C;%5E%7B%5Ccirc%7D%5Cmathrm%7BC%7D%7D%7D%20=%20272.02" title="c_{\mathrm{air}} = 331.3 \mathrm{m \cdot s^{-1}} \sqrt{1+\frac{-89}{273.15\;^{\circ}\mathrm{C}}} = 272.02">

The difference is 364.78 - 272.02 = 92.76 m/s

<img src="/cgi-bin/mimetex.cgi?c_%7B%5Cmathrm%7Bair%7D%7D%20=%20331.3%20%5Cmathrm%7Bm%20%5Ccdot%20s%5E%7B-1%7D%7D%20%5Csqrt%7B1+%5Cfrac%7BT%7D%7B273.15%5C;%5E%7B%5Ccirc%7D%5Cmathrm%7BC%7D%7D%7D" title="c_{\mathrm{air}} = 331.3 \mathrm{m \cdot s^{-1}} \sqrt{1+\frac{T}{273.15\;^{\circ}\mathrm{C}}}">

Thus at T = 58°C:

<img src="http://latex.codecogs.com/gif.latex?c_%7B%5Cmathrm%7Bair%7D%7D%20=%20331.3%20%5Cmathrm%7Bm%20%5Ccdot%20s%5E%7B-1%7D%7D%20%5Csqrt%7B1+%5Cfrac%7B58%7D%7B273.15%5C;%5E%7B%5Ccirc%7D%5Cmathrm%7BC%7D%7D%7D%20=%20364.78" title="c_{\mathrm{air}} = 331.3 \mathrm{m \cdot s^{-1}} \sqrt{1+\frac{58}{273.15\;^{\circ}\mathrm{C}}} = 364.78">

At T = -89°C:

<img src="http://latex.codecogs.com/gif.latex?c_%7B%5Cmathrm%7Bair%7D%7D%20=%20331.3%20%5Cmathrm%7Bm%20%5Ccdot%20s%5E%7B-1%7D%7D%20%5Csqrt%7B1+%5Cfrac%7B-89%7D%7B273.15%5C;%5E%7B%5Ccirc%7D%5Cmathrm%7BC%7D%7D%7D%20=%20272.02" title="c_{\mathrm{air}} = 331.3 \mathrm{m \cdot s^{-1}} \sqrt{1+\frac{-89}{273.15\;^{\circ}\mathrm{C}}} = 272.02">

The difference is 364.78 - 272.02 = 92.76 m/s

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