Respuesta :
Answer : The unit of (D) in metric system is [tex]m^2/s[/tex]
Explanation :
The given expression is:
[tex](dm/dt)=(-2\pi)\times (d)\times (D)\times (\frac{M}{RT})\times P[/tex]
where,
m = mass
t = time
d = diameter
D = diffusion coefficient
M = molar mass
R = universal gas constant
T = temperature
P = partial pressure
In metric system,
The unit of mass is, kg
The unit of time is, s
The unit of diameter is, m
The unit of molar mass is, kg/mol
The unit of universal gas constant is, [tex]Nm/^oC.mol[/tex]
The unit of temperature is, [tex]^oC[/tex]
The unit of partial pressure is, [tex]N/m^2[/tex]
The unit of diffusion coefficient will be:
[tex]D=\frac{(dm/dt)}{(-2\pi)\times (d)\times (\frac{M}{RT})\times P}[/tex]
or,
[tex]D=\frac{(dm)\times (R)\times (T)}{2\pi \times (d)\times (dt)\times (M)\times (P)}[/tex]
[tex]D=\frac{(dm)\times (R)\times (T)}{(d)\times (dt)\times (M)\times (P)}[/tex]
Now put all the unit in this expression, we get:
[tex]D=\frac{(kg)\times (Nm/^oC.mol)\times (^oC)}{(m)\times (s)\times (kg/mol)\times (N/m^2)}[/tex]
[tex]D=m^2/s[/tex]
Therefore, the unit of (D) in metric system is [tex]m^2/s[/tex]
