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Using the following data, find the chang...

Using the following data, find the change in temperature at which wood will just sink in benzene.
Density of benzene at `0^(@)C=9xx10^(2)kgm^(-3)`,
Density of wood at `0^(@)C=8.8xx10^(2)kgm^(-3)`,
Cubical expansivity of benzene `=1.2xx10^(-3)K^(-1)`
Cubical expansivity of wood `=1.5xx10^(-4)K^(-1)`

Text Solution

Verified by Experts

Let the subscript `1` and `2` denotes benzene and wood, respectively.
`:. (rho_(1))/(1+gamma_(1)DeltaT)=(rho_(2))/(1+gamma_(2)DeltaT)`
or `rho_(1)+rho_(1)gamma_(2)DeltaT=rho_(2)+rho_(2)gamma_(1)DeltaT`
or `DeltaT=(rho_(1)-rho_(2))/(rho_(2)gamma_(1)-rho_(1)gamma_(2))`
Here, `rho_(1)=900kgm^(3)`, `rho_(2)=880kg//m^(3)` , `gamma_(1)=1.2xx10^(-3)K^(-1)` ,
`gamma_(2)=1.5xx10^(-4)K^(-1)`
`:. DeltaT=21.7^(@)C`
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Using the following data, calculate at what temperature will the wood just sink in benzene Density of wood at 0^(@) C = 8.8 xx 10^(2)kg//m^(3) Density of benzene at 0^(@) C = 9 xx 10^(-4)K^(-1) Cubical expansivity of wood = 1.5 xx 10^(-4)K^(-1) Cubical expansivity of benzene = 1.2 xx 10^(-3)K^(-1)

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Knowledge Check

  • Using the following data, calculate at what temperature will the wood just sink in benzene? Density of wood at 0^(@)C= 8.8 xx 10^(2)kg//m^(3) Density of benzene at 0^(@)C = 9 xx 10^(2) kg//m^(3) Cubical expansivity of wood =1.5 xx 10^(-4) K^(-1) Cubical expansivity of benzene =1.2 xx 10^(-3) K^(-1)

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