Question
Attached is the problem, please show step by step work with formula and some explaination
The spirit-in-glass thermometer, invented in Florence, Italy, around 1654, consists of a tube of liquid (the spirit) containing a number of submerged glass spheres with slightly different masses (Fig. P14.76). At sufficiently low temperatures, all the spheres float, but as the temperature rises, the spheres sink one after another. The device is a crude but interesting tool for measuring temperature. Suppose the tube is filled with ethyl alcohol, whose density is 0.789 45 g/cm3 at 20.0 degree C and decreases to 0.780 97 g/cm3 at 30.0 degree C. (a) Assuming that one of the spheres has a radius of 1.000 cm and is in equilibrium halfway up the tube at 20.0degree C, determine its mass. (b) When the temperature increases to 30.0degree C, what mass must a second sphere of the same radius have to be in equilibrium at the halfway point? (c) At 30.0 degree C, the first sphere has fallen to the bottom of the tube. What upward force does the bottom of the tube exert on this sphere?
Explanation / Answer
a) since it is in equilibriun
mg=V*rho*g
at 20 degree C ...rho=0.78945 g/cc
==> m=V*rho=4*pi*R^3*rho/3=3.305 gm
b) at 30 degree C
rho=0.78097 g/cc
fot this to be in equilibriun
m=V*rho1=4*pi*R^3*rho1/3=3.26966 gm
c) Upward force exerted at the bottom=V*(rho1-rho2)*g=4*pi*R^3*(rho1-rho2)*g/3=3.479 E-4 N
