Operating instructions

METTLER TOLEDO DE40/50/51 Density Meter 9
Density
The period of oscillation T is obtained from the equation:
ρ = Density of sample in measurement tube [g/cm
3
]
V
c
= Volume of sample (capacity of tube) [cm
3
]
m
c
= Mass of measurement tube [g]
K = Measurement tube constant [g/s
2
]
It follows that
The density and the period of oscillation T are related as follows:
ρ = A T
2
+ B (see illustration)
A and B are constants which are determined by the elasticity, structure and mass of the
measurement tube. As the mass varies from tube to tube, it must be determined by
measurement. We refer to this as a factor determination or adjustment of the instrument. The
factor of the measurement tube is calculated by measuring the period of oscillation T of two
standard substances of known density, e.g. air and water:
ρ
A
= Density of air [g/cm
3
]
ρ
W
= Density of water [g/cm
3
]
T
A
= Period of oscillation of the air measurement [s]
T
W
= Period of oscillation of the water measurement [s]
The unknown density of a substance ρ
S
is calculated after the factor
determination by measurement of its
period of oscillation using the following
formula:
F (T
A
2
– T
S
2
) = ( ρ
A
– ρ
S
)
Solving for ρ
S
gives:
ρ
S
= ρ
A
– F (T
A
2
– T
S
2
)
Note: The factor is temperature dependent. The volume of the measurement tube and its
period of oscillation change with temperature. It is thus necessary to determine the
factor of the cell for the temperature at which you measure your samples!
ρ
A
= 0.00120
T
2
ρ
ρ
W
= 0.99821
ρ
S
T
S
2
T
W
2
T
A
2
T = 2π
ρV
c
+ m
c
K
ρ =
4π
2
V
c
K
T
2
–
V
c
m
c
F =
4π
2
V
c
K
T
A
2
–
T
W
2
ρ
A
–
ρ
W
=