Argon gas is filled in two identical bottles X and Y. The mass of the gas in the two bottles is $5$ gm and $25$ gm respectively. If the speed of sound is the same in both bottles, what conclusions will you draw?

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Solution

Mass of Argon in bottle $X = M_{1} = 5 g$
Mass of Argon in bottle $Y = M_{2} = 25 g$
Given $V_{1} = V_{2}$ & $V \propto \frac{\sqrt{T}}{\sqrt{M}}$
$∴ \frac{\sqrt{T_{1}}}{\sqrt{M_{1}}} = \frac{\sqrt{T_{2}}}{\sqrt{M_{2}}}$
$\Rightarrow \frac{T_{1}}{M_{1}} = \frac{T_{2}}{M_{2}}$
$∴ \frac{T_{1}}{5} = \frac{T_{2}}{25}$ or $T_{2} = 5 T_{1}$
i.e. Temperature of bottle $Y$ is $5$ times that of bottle $X$ .

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Argon gas is filled in two identical bottles X and Y. The mass of the gas in the two bottles is 5gm and 25gm respectively. If the speed of sound is the same in both bottles, what conclusions will you draw?

Mass of Argon in bottle X=M1=5gMass of Argon in bottle Y=M2=25gGiven V1=V2 & V∝√T√M∴√T1√M1=√T2√M2⇒T1M1=T2M2∴T15=T225 or T2=5T1i.e. Temperature of bottle Y is 5 times that of bottle X.

Argon gas is filled in two identical bottles X and Y. The mass of the gas in the two bottles is $5$ gm and $25$ gm respectively. If the speed of sound is the same in both bottles, what conclusions will you draw?