A piece of wood of density 0.8 gmcmfloats in a liquid of density 0.9 gmcm^(-3)at 0^(@)C. At what temperature does the piece of wood sink in the liquid (gamma _(R ) = 8.5 xx 10 ^(-5) //^(@)C and coefficient of expansion of liquid Y_(R ) = 1.2 xx 10 ^(-3) //^(@)C)

A piece of wood of density 0.8 gmcmfloats in a liquid of density 0.9 g

1.	A piece of wood of density 0.8 gmcmfloats in a liquid of density 0.9 gmcm^(-3)at 0^(@)C. At what temperature does the piece of wood sink in the liquid (gamma _(R ) = 8.5 xx 10 ^(-5) //^(@)C and coefficient of expansion of liquid Y_(R ) = 1.2 xx 10 ^(-3) //^(@)C)
Answer» Solution :Let the piece of wood sink in the liquid at `t ^(@)C.` From `d _(0) = d _(t) [1 + gamma _(R) t ]` Density of the liquid at `t ^(@) C: d _(0)` (liquid) `= d _(t) ` (liquid) `[1 + gamma _(R) t ] (or d _(t)` (liquid) `= (d _(0) ("liquid"))/(1 + gamma _(R) t ) and d _(t) ` (wood) ` = (d_(0) ("wood"))/( 1 + gamma _(R) t ) ,` For the wood to sink, Density of liquid at `t ^(@)C=` Density of wood `t ^(@)C` `(d _(0) ("liquid"))/( 1 + gamma _(R) t ) = (d _(0) ("wood"))/( 1 + gamma _(OMEGA t )) = (0.9 )/( 1 + 1.2 xx 10 ^(-3) t) = (0.8)/( 1 + 8.5 xx 10 ^(-5) t ) = 0.9 xx 8.5 xx 10 ^(-5) t = 0.8 + 0.8 xx 1.2 xx 10 ^(-3) t` `0.9 + 0.000 765t = 0.8 + 0.00096t , t[ 0.0096-0.000765] =-.9 -0.8 , t = (0.1)/( 0.008835) = 113.19^(@)C`