Oxygen and helium are each kept at and the same pressure in two separate vessels

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

Problem

Oxygen and helium are each kept at 300 K300\,\text{K} and the same pressure in two separate vessels. For oxygen take MO2=32 g mol−1M_{\text{O}_2}=32\,\text{g\,mol}^{-1} and γO2=1.40\gamma_{\text{O}_2}=1.40; for helium take MHe=4.0 g mol−1M_{\text{He}}=4.0\,\text{g\,mol}^{-1} and γHe=1.66\gamma_{\text{He}}=1.66. (i) Calculate the speed of sound in oxygen under the stated conditions. (ii) Calculate the speed of sound in helium under the same conditions. (iii) Find the ratio vHe/vO2v_{\text{He}}/v_{\text{O}_2} and explain, with reference to molecular properties, why the two speeds differ so markedly.

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