At and pressure

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

At T=300 KT = 300\,\text{K} and pressure 1.01×105 Pa1.01\times10^{5}\,\text{Pa}, two different gases—helium and carbon dioxide—are kept in separate long tubes. Universal gas constant R=8.314 J mol−1K−1R = 8.314\,\text{J\,mol}^{-1}\text{K}^{-1}. The molar masses and specific–heat ratios are: Helium: MHe=4.0 g mol−1M_{\text{He}} = 4.0\,\text{g\,mol}^{-1}, γHe=1.67\gamma_{\text{He}} = 1.67 Carbon dioxide: MCO2=44.0 g mol−1M_{\text{CO}_2} = 44.0\,\text{g\,mol}^{-1}, γCO2=1.29\gamma_{\text{CO}_2} = 1.29 (i) Using an appropriate formula, calculate the speed of sound in helium under the given conditions. (ii) Repeat the calculation for carbon dioxide. (iii) Compare the two results obtained and explain, with reference to the parameters involved, why helium supports a much higher speed of sound than carbon dioxide.

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