A large vessel contains an equimolar mixture of helium (molar mass 4 g mol ) and…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A large vessel contains an equimolar mixture of helium (molar mass 4 g mol

^{-1}

) and nitrogen (molar mass 28 g mol

^{-1}

) at 300 K. Assume that both gases behave ideally and that the ratio of specific heats

\gamma

is the same for each gas and for their mixture. (i) Determine the effective molar mass

M_{\text{mix}}

of the mixture. (ii) Prove that the speed of sound in the mixture is related to that in pure nitrogen,

v_{\text{N}_2}

, by the relation

\dfrac{v_{\text{mix}}}{v_{\text{N}_2}} = \sqrt{\dfrac{M_{\text{N}_2}}{M_{\text{mix}}}}.

(iii) Using your result, calculate

\dfrac{v_{\text{mix}}}{v_{\text{N}_2}}

and state whether the mixture transmits sound faster or slower than pure nitrogen kept at the same temperature.