Determine the change in volume of 6 liters of alcohol (in cm3) if the pressure is decreased from 200 cm of Hg to 75 cm. (velocity of sound in alcohol is 1250 m/s, density of alcohol = 0.80 gm/cc, density of Hg = 13.6 gm/cc and g = 10 m/s2)
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answer is 0.82.
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Detailed Solution
The velocity of sound in liquid v=Bρ⇒B=v2ρBut by definition B=−ΔP(ΔV/V)Hence −VΔPΔV=v2ρ, i.e. ΔV=V(−ΔP)ρv2Here ΔP=H2ρg−H1ρg=(75−200)×13.6×1000 =−1.7×106 dynes /cm2So ΔV=6×1031.7×1060.80×1.25×1052=0.82cc