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Question

The loss of weight of a solid when immersed in a liquid at 0C is W0 then the loss of weight W at tC is - where α and β are the cubical expansion coefficients of solid and liquid respectively.


Solution

The correct option is A
Let Ws be the weight of the solid and ds be the density at 0C. Let dL be the density of the liquid at that temperature.
The loss of weight of solid when immersed in the liquid at 0C.
=(Wsds)d1=W0  (given)(1)
Similarly, the loss of weight of the solid when immersed in the liquid at tC.
=(Wsds)×dL=W (given)(2)
where \(d^{'}_{s}\) = density of solid at tC.
and \(d^{'}_{L}\) = density of liquid at tC.
Now ds and \(d^{'}_{s}\) are related as
ds=ds1+αtSimilarly, dL=dL(1+βt)
where α and β are the coefficients of cubical expansion of the solid and the liquid respectively.
Now equation (2) can be written as
Ws×1+αtds×dL1+βt=Wor (Wsds×dL)(1+αt1+βt)=Wor, W01+αt1+βt=W   [from (1)]or, W0(1+αt)(1+βt)1=Wor, W0(1+αt)(1βt)=W    (approx)or, W0[1+(αβ)tαβt2]=Wor, W0[1+(αβ)t]=W (approx)
 

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