The density at 25 degrees is [tex]1.35\cdot 10^4 kg/m^3[/tex]
Explanation:
The density of a material is given by
[tex]d=\frac{m}{V}[/tex]
where
m is its mass
V is its volume
The volume of a material changes as a function of the temperature, according to
[tex]V(T)=V_0(1+\alpha (T-T_0))[/tex]
where
[tex]V_0[/tex] is the volume at temperature [tex]T_0[/tex]
[tex]\alpha[/tex] is the coefficient of volume expansion
In this problem, let's take a sample of mercury of mass
m = 1 kg
The density at 0 degrees is
[tex]d_0 = 1.36\cdot 10^4 kg/m^3[/tex]
So the corresponding volume is
[tex]V_0 = \frac{m}{d_0}=\frac{1}{1.36\cdot 10^4}=7.35\cdot 10^{-5} m^3[/tex]
For mercury,
[tex]\alpha = 2.8\cdot 10^{-4} ^{\circ}C^{-1}[/tex]
So the volume when [tex]T=25^{\circ}C[/tex] is
[tex]V(25)=(7.35\cdot 10^{-5})(1+2.8\cdot 10^{-4}(25-0))=7.4\cdot 10^{-5} m^3[/tex]
And since the mass has not changed, we can now calculate the density at 25 degrees:
[tex]d_{25}=\frac{m}{V_{25}}=\frac{1}{7.4\cdot 10^{-5} m^3}=1.35\cdot 10^4 kg/m^3[/tex]
Learn more about density:
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