(a) In the previous example, determine the temperature rise at which the solid is completely immersed, neglect expansion of solid? (b) if, f _(s1) and f_(s2) are the fractions submerged for rise of temperatures, Delta T and Delta T_(2), determine yof the liquid (c) Under what conditions will the sphere sink, lift up, considering expansion of solid?

(a) In the previous example, determine the temperature rise at which t

1.	(a) In the previous example, determine the temperature rise at which the solid is completely immersed, neglect expansion of solid? (b) if, f _(s1) and f_(s2) are the fractions submerged for rise of temperatures, Delta T and Delta T_(2), determine yof the liquid (c) Under what conditions will the sphere sink, lift up, considering expansion of solid?
Answer» Solution :(a) From previous problem, `f _(s) = (rho)/(sigma),` When the temperature is INCREASED by `Delta T.` `f _(s) . = 1 = f _(s) (1 + gamma Delta T) or Delta T = (1 - f _(s))/( gamma f _(s))` (B)`f _(s _(t)) = f _(s) (1 + gamma Delta T _(1)), f _(s), = f _(s) (1 + gamma Delta T _(2)) implies (f _(s _(1)))/( f _(s _(2))) = ((1 + gamma Delta T _(1))/( 1 + gamma Delta T _(2)))` On solving for `gamma,` we have `gamma = (f _(s _(1))- f _(s _(2)))/( f _(s _(2))Delta -f _(s _(1)) Delta T _(2))` (C ) As `f _(s) = (rho )/(sigma ) and f _(s) . = (rho .)/( sigma .) = ((rho )/( 1 + gamma _(1) Delta T )) ((1 + gamma _(2) Delta T ))/( sigma) =f _(s) ((1 + gamma _(2) Delta T )/( 1 + gamma _(1) Delta T ))` If ` gamma _(2) gtgamma _(1),` the solid sinks, If `gamma _(2) = gamma _(1),` no EFFECT on submergence. `If gamma _(2) lt gamma _(1),` the solid lifts up.