Question

What are the units of (D) when... m is the mass, t is time, d is the diameter, D is the diffusion coefficient, M is the molar mass, R is the universal gas constant, T is the temperature, and P is the partial pressure.... (dm/dt) = (-2pi)*(d)*(D)*(M/(RT))*P

Answer 1

Answer : The unit of (D) in metric system is
`m^2/s`

Explanation :

The given expression is:

`(dm/dt)=(-2\pi)* (d)* (D)* ((M)/(RT))* P`

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,
`Nm/^oC.mol`

The unit of temperature is,
`^oC`

The unit of partial pressure is,
`N/m^2`

The unit of diffusion coefficient will be:

`D=((dm/dt))/((-2\pi)* (d)* ((M)/(RT))* P)`

or,

`D=((dm)* (R)* (T))/(2\pi * (d)* (dt)* (M)* (P))`

`D=((dm)* (R)* (T))/((d)* (dt)* (M)* (P))`

Now put all the unit in this expression, we get:

`D=((kg)* (Nm/^oC.mol)* (^oC))/((m)* (s)* (kg/mol)* (N/m^2))`

`D=m^2/s`

Therefore, the unit of (D) in metric system is
`m^2/s`