Fractional change in density of mercury

[ams0101]

Homework Statement

What is the fractional change in the density of mercury when temperature changes for 30oC to -10oC. The density of mercury at 30oC is 13600 kgm-3.

Homework Equations

dt=do(1-gamma t)

The Attempt at a Solution

gamma=180x10^-6
t=30
dt=13600
13600=do(1-180x10^-6*30)
do=13600/(1-180x10^-6*30)
do=13673.839

gamma=180x10^-6
t=-10
do=13673.839
dt= ?
dt=13673.839 (1-180x10^-6*-10)
dt=13698.45

fractional change = 13600/13698.45

I just don't think that I am understanding this properly...

 

[anathema]

Thank you for your question. I can provide you with the correct solution to your problem.

The density of a substance is directly proportional to its temperature, which means that as the temperature increases, the density also increases. This relationship is described by the formula:

p = p0 (1 + γΔT)

Where p is the density at a given temperature, p0 is the density at a reference temperature, γ is the coefficient of thermal expansion, and ΔT is the change in temperature.

In your case, the reference temperature is 30oC and the change in temperature is -40oC (since 30oC to -10oC is a decrease of 40oC). The coefficient of thermal expansion for mercury is 180x10^-6, as you correctly stated.

Plugging in the values, we get:

p = 13600 kgm^-3 (1 + 180x10^-6 x (-40))
p = 13600 kgm^-3 (1 - 0.0072)
p = 13499.2 kgm^-3

Therefore, the density of mercury at -10oC is approximately 13499.2 kgm^-3.

To calculate the fractional change in density, we use the formula:

Fractional change = (p - p0)/p0

Where p is the density at the new temperature and p0 is the density at the reference temperature.

Plugging in the values, we get:

Fractional change = (13499.2 kgm^-3 - 13600 kgm^-3)/13600 kgm^-3
Fractional change = -0.0074

Therefore, the fractional change in density of mercury when the temperature changes from 30oC to -10oC is approximately -0.74%.

I hope this helps clarify the concept for you. If you have any further questions, please do not hesitate to ask.

Scientist