Question

A solid whose volume does not change with temperature, floats in a liquid. Fractions f1 and f2 of its volume remain submerged for two different temperatures t1 and t2of liquid. The volume coefficient of expansion of liquid is:​

Answer 1

Let the volume of a solid is V.

fraction f1 of its volume remains submerged for temperature t1 of liquid.

so, V1 = V[1 + y t1]

where y is volume coefficient of expansion of liquid.

or, f1V = V [ 1 + yt1 ]

or, f1 = [1 + yt1 ] ........(1)

similarly, fraction f2 of its volume remain submerged for temperature t2 of liquid.

so, V2 = V[1 + yt2 ]

or, f2V = V[1 + yt2]

or, f2 = [1 + yt2 ] .......(2)

from equations (1) and (2),

f1/f2 = [1 + yt1]/[1 + yt2]

or, f1(1 + yt2) = f2(1 + yt1)

or, f1 + f1.y.t2 = f2 + f2.y.t1

or, (f1 - f2) = f2.y.t1 - f1.y.t2

or, y(f2.t1 - f1.t2) = (f1 - f2)

or, y = (f1 - f2)/(f2.t1 - f1.t2)

hence, volume coefficient of expansion of liquid is y = (f1 - f2)/(f2.t1 - f1.t2)

Answer 2

Answer:

Let the volume of a solid is V.

fraction f1 of its volume remains submerged for temperature t1 of liquid.

so, V1 = V[1 + y t1]

where y is volume coefficient of expansion of liquid.

or, f1V = V [ 1 + yt1 ]

or, f1 = [1 + yt1 ] ........(1)

similarly, fraction f2 of its volume remain submerged for temperature t2 of liquid.

so, V2 = V[1 + yt2 ]

or, f2V = V[1 + yt2]

or, f2 = [1 + yt2 ] .......(2)

from equations (1) and (2),

f1/f2 = [1 + yt1]/[1 + yt2]

or, f1(1 + yt2) = f2(1 + yt1)

or, f1 + f1.y.t2 = f2 + f2.y.t1

or, (f1 - f2) = f2.y.t1 - f1.y.t2

or, y(f2.t1 - f1.t2) = (f1 - f2)

or, y = (f1 - f2)/(f2.t1 - f1.t2)

hence, volume coefficient of expansion of liquid is y = (f1 - f2)/(f2.t1 - f1.t2)