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Two monoatomic gases of equal masses are in two different containers at S.T.P. if the ratio of velocities of sound in them is `1 :2` , then find the ratio of their volumes . |
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Answer» Ratio of the velocities of sound in them = `1:2` we know that velocity of sound in a gas is inversely proportional to square root of molecular weight . `therefore V porp (1)/(sqrtM)` `M prop (1)/(V^(2))` `(M_(1))/(M_(2)) = ((V_(2))/(V_(1)))^(2) = ((2)/(1))^(2) = 4 :1` But PV = n.RT `V = nR((T)/(p))` `V prop (m)/(M) [ because T, p and R` are constant and n = `(m)/(M)`] `therefore V prop (1)/(M) [ therefore` m is also constant ] `therefore (V_(1))/(V_(2)) = (M_(2))/(M_(1)) = 1 :4` Alternate method : `V prop (1)/(sqrtd) ` or `V prop (1)/(sqrt((m)/(V)))` or `(V_(1))/(V_(2)) = sqrt((V_(1))/(V_(2)))` `therefore (V_(1)^(1))/(V_(2)^(1)) = (V_(1)^(2))/(V_(2)^(2)) = (1)/(2^(2)) = (1)/(4)` |
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