I have been working on this problem, and I am stuck. The problem is: Use the def

Question

I have been working on this problem, and I am stuck. The problem is: Use the definition for coefficient of volume expansion ? = - to show that the change in density Delta P of a substance when temperature changes by Delta Theta is given by Delta P = yp = -yp Delta Theta . What is the fraction change in the density of mercury when temperature changes for 30? Degree C to -10 Degree C. The density of mercury at 30 Degree C is 13600 kgm^-3 I arranged these equations and got , but it does not help to get the fraction change in the density of mercury when it's temperature changed 40 degrees. Please help!

Explanation / Answer

EDIT: sorry did not see that someone had already answered the question. Please disregard this post

gamma = dV / (V*dTheta)

Volume = mass*density

Because mass is never destroyed, a change in volume corresponds to a direct change in density

d(Volume) = d(mass*density) = mass*d_density

d_V = mass*d_density

Divide this equation by V = mass*density

d_V/V = mass*d_density / (mass*density)
d_V/V = d_density/densitry

From the definition, gamma = (d_V/V)/d_T,

gamma = d_density/ density / d_T.

Rearrange this equation,


d_density/ density = gamma*d_T


d_T = 40 celsius

gamma is not given. Do you have a text to refer to this value. Otherwise, I just looked it up online:

For mercury, gamma = 181e-6/K


Thus, d_density/density = 181*10^-6 * 40 = 0.00724.

percent change = 0.00724*100% = 0.724%



Good Luck

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