Respuesta :
Answer:
a) The mass of the blood is 5.788 kg
b) The total cells is 1.041x10¹³cells
Explanation:
Given:
V = volume of blood = 5.46 L = 0.00546 m³
ρ = density of blood = 1060 kg/m³
a) The mass of the blood is equal:
[tex]\rho =\frac{m}{V} \\m=\rho V=1060*0.00546=5.788kg[/tex]
b) mc = mass of cells = 45% of mass of blood
mc = 0.45 * 5.788 = 2.6046 kg
ρc = density of cells = 1125kg/m³
The volume of the cells:
[tex]V_{c} =\frac{m_{c} }{\rho _{c} } =\frac{2.6046}{1125} =0.0023m^{3}[/tex]
Vwc = volume of white blood cells = 1% of volume of the cells
Vwc = 0.01 * 0.0023 = 2.3x10⁻⁵m³
The radius of the cell is:
[tex]r_{c} =\frac{7.5x10^{-6} }{2} =3.75x10^{-6} m[/tex]
The volume of a single cell is:
[tex]V_{sc} =\frac{4\pi r^{3} }{3} =\frac{4\pi (3.75x10^{-6})^{3} }{3} =2.209x10^{-16} m^{3}[/tex]
The number of the red blood cells is:
[tex]N_{rc} =\frac{0.0023-2.3x10^{-5} }{2.209x10^{-16} } =1.031x10^{13} cells[/tex]
The number of the white blood cells is:
[tex]N_{wc} =\frac{2.3x10^{-5} }{2.209x10^{-16} } =1.041x10^{11} cells[/tex]
The total cells is:
Tc = 1.031x10¹³ + 1.041x10¹¹ = 1.041x10¹³cells
This question involves the concepts of the density, mass, and volume.
a. The mass of the blood in Jeff's body is "5.79 kg".
b. The no. of white blood cells and red blood cells are "1.05 x 10¹¹" and "1.04 x 10¹³" in Jeff's body, respectively, with the total number of cells "1.052 x 10¹³".
a.
The formula of density can be used to find out the mass of the blood:
[tex]\rho=\frac{m}{V}\\\\m =\rho V[/tex]
where,
m = mass of the blood = ?
[tex]\rho[/tex] = density of the blood = 1060 kg/m³
V = volume of the blood = 5.46 L = 5.46 x 10⁻³ m³
Therefore,
m = (1060 kg/m³)(5.46 x 10⁻³ m³)
m = 5.79 kg
b.
First, we will find out the volume of the cells:
[tex]V_c=\frac{m_c}{\rho_c}[/tex]
where,
[tex]V_c[/tex] = volume of the cells = ?
[tex]m_c[/tex] = mass of the cells = 45% of V = (0.45)(5.79 kg) = 2.61 kg
[tex]\rho_c[/tex] = density of the cells = 1125 kg/m³
Therefore,
[tex]V_c=\frac{2.61\ kg}{1125\ kg/m^3}\\\\V_c=2.316\ x\ 10^{-3}\ m^3[/tex]
Now, the volume of white blood cells will be:
[tex]V_{wc}=1\%\ of V_c = (0.01)(2.316\ x\ 10^{-3}\ m^3)\\\\V_{wc}=2.316\ x\ 10^{-5}\ m^3[/tex]
The volume of a single cell modeled as a sphere is:
[tex]V_{sc}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\frac{7.5\ x\ 10^{-6}m}{2})^3\\\\V_{sc}=2.2\ x\ 10^{-16}\ m^3[/tex]
Correction: diameter is given in micrometers not meters.
Now, the number of white blood cells can be given by the following formula:
[tex]N_{wbc}=\frac{V_{wc}}{V_{sc}}=\frac{2.316\ x\ 10^{-5}\ m^3}{2.2\ x\ 10^{-16}\ m^3}\\\\N_{wbc} = 1.05\ x\ 10^{11}\ cells[/tex]
Now, the number of red blood cells can be given by the following formula:
[tex]N_{rbc}=\frac{V_c-V_{wc}}{V_{sc}}=\frac{231.6\ x\ 10^{-5}\ m^3-2.316\ x\ 10^{-5}\ m^3}{2.2\ x\ 10^{-16}\ m^3}\\\\N_{rbc} = 104.2\ x\ 10^{11}\ cells[/tex]
Total number of cells in Jeff's body are:
[tex]N=N_{wbc}+N_{rbc}\\N=1.05\ x\ 10^{11}+104.2\ x\ 10^{11}\\N=1.052\ x\ 10^{13}\ cells[/tex]
Learn more about density here:
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