Atmospheric air can be treated as either perfectly dry or moderately moist

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

Problem

Atmospheric air can be treated as either perfectly dry or moderately moist. At a given pressure, the ratio of specific heats for dry air is

\gamma_{\text{dry}}=1.40

while for moist air it is

\gamma_{\text{moist}}=1.33

. (i) Derive an expression for the ratio

\dfrac{v_{\text{moist}}}{v_{\text{dry}}}

of the speeds of sound in moist air and dry air at the same absolute temperature. (ii) Dry air at

30\,^{\circ}\!\text{C}

carries sound at

349\,\text{m\,s}^{-1}

. Determine the temperature (in

^\circ\!\text{C}

) to which moist air must be heated so that the speed of sound in it becomes equal to

349\,\text{m\,s}^{-1}

. State all steps clearly.