A long horizontal tube is divided by a thin

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

Problem

A long horizontal tube is divided by a thin, freely-moving partition into two equal sections. Section A contains gas A with

M_{A}=28\,\text{g\,mol}^{-1}

and

\gamma_{A}=1.40

; section B contains gas B with unknown molar mass

M_{B}

and

\gamma_{B}=1.30

. Both gases are at

300\,\text{K}

and the same pressure. When short sound pulses are generated in each section, the measured speeds are

v_{A}=340\,\text{m\,s}^{-1}

and

v_{B}=260\,\text{m\,s}^{-1}

respectively. (i) Determine the molar mass

M_{B}

of gas B. (ii) After the partition is removed and the gases mix thoroughly at the same temperature and pressure, the mixture behaves ideally with an effective ratio of specific heats

\gamma_{\text{mix}}=1.35

and an average molar mass equal to the arithmetic mean of

M_{A}

and

M_{B}

. Calculate the approximate speed of sound in the mixture. (iii) Discuss briefly how the differing values of

\gamma

and molar mass influence the speed obtained in part (ii).

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