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True mass & conventional mass
Succinct definition
"True mass" or "mass in a vacuum"
The quantity of matter composing a given object.
Mass in the Newtonian sense.

Conventional mass
Conventional mass is the mass that an object would appear to have if weighed at 20 degree C in air of density of 1.2 mg/cm3 against a standard having a density of 8.0 g/cm3. It is the mass an object would appear to have under the above conditions.

Note:
In order to calculate the conventional mass, you must know the air density of the environment in which the mass measurement was taken. The Oregon Metrology Laboratory uses the CIPM (Comite International des Poids et Mesures) formula, along with environmental measurements of temperature, humidity and barometric pressure, to calculate the lab air density.

Expanded definition
To understand the difference between "true mass" and "conventional mass" we must first be clear on what we mean by the terms mass, volume and density. Mass is the quantity of matter composing an object. In essence it's the amount of stuff. Volume is the amount of space the object fills, and density is the mass divided by the volume. Thus, an object composed of more stuff is more dense than an object of the same size composed of less stuff. Two objects of different volumes can have the same mass if the density of the smaller object is greater than that of the larger (and in the right proportion). Likewise, two objects of the same volume will have different masses if their densities are not the same.

"True mass" or "mass in a vacuum"
"True mass," or "mass in a vacuum" is what the name implies. It is the mass of the object. So what is this "Conventional Mass" and why do we even bother with it?

"Conventional mass"
"Conventional mass" is the mass an object would appear to have if it was weighed at 20 degree C in the air density 1.2 mg/cm3 against a standard of density 8.0 g/cm3. Why 8.0 g/cm3?  Why 20 degree C? Why in air of density 1.2 mg/cm3? These are all arbitrary values chosen for ease. There needed to be some sort of reference standard for mass measurements. The density of the object was set to 8.0 g/cm3 because most mass standards have a density of 8.0 g/cm3 or something very close. Your typical office or lab environment is maintained near 20 degree C, and thus most weighings are conducted at 20 degree C or some temperature close to it. And in most places at most times, the air density is 1.2 mg/cm3.

If you are still unsure about "conventional mass", read on.
Like water, air has mass. A certain volume of air will have a certain mass depending on the air density. And like water, displaced air results in a buoyant or lifting force. It is this lifting force that explains why we feel "lighter" in a pool than we do on land and why ships weighing several tons can still float. An object in water experiences an upward force equal to the weight of the water displaced by the object. Likewise, an object in air experiences an upward force equal to the weight of the air displaced by the object.

Consider an object at rest on a balance in a vacuum. It will experience a downward gravimetric force equal to the mass (or "true mass") of the object times the acceleration due to gravity. The object will press down on the balance with this force and the balance will indicate the object´s true mass.
 
Now imagine this same object at rest on a balance in air. The object will experience the downward gravimetric force as well as the upward force of air buoyancy.
 

 
The resulting force with which the object presses down on the balance is less than the gravimetric force on the object by an amount equal to the air buoyant force. The balance does not know whether the object is in a vacuum or in air, and thus it will indicate that the object is less massive than before. The mass of the object will appear to be less.

Imagine this same object on an equal arm balance in a vacuum. It is perfectly balanced by a standard of density 8.0 g/cm3. Thus, the standard and the object have the same "true mass."
 

Now imagine that same object and standard balanced at 20 degree C in air of density 1.2 mg/cm3. If the object has a density different from 8.0 g/cm3, then for it to have the same "true mass" as the standard, it must not have the same volume. Both the object and the standard experience the downward force of gravity equal to their true mass times the acceleration due to gravity. However, since their volumes are different, the amount of air displaced by the object is different from that displaced by the standard, and hence the weight of air displaced by the object is different from the weight of air displaced by the standard.

 
Thus, the lifting force on the object and that on the standard are not the same and the object will no longer appear to have the same mass as the standard. The mass that the object now appears to have is the "conventional mass".
 

Applying results
Applying laboratory results to your business setting
The conventional mass of a given weight is found by adding the conventional mass correction, as listed on laboratory calibration reports, to the weight´s declared nominal value. A positive correction indicates that the conventional mass of the weight is larger than the stated nominal value, while a negative correction indicates that the mass value is smaller. Under most weighing conditions, the conventional mass correction should be applied since it accounts for the effect of normal air. However, if you are using the weight in an environment with an air density significantly different from 1.2 mg/cm3, you should use the true mass value along with air buoyancy corrections to determine the weights appropriate mass value. For more information on calculating air buoyancy corrections, or to enquire whether the conventional mass is applicable to your weighing setting, please contact the Metrology Laboratory.

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