# Relationship between Mass and Conventional Mass

The buoyant effect of air on an object always acts against gravity.

Air is always exerting a lifting effect on all objects. The magnitude of that effect is directly proportional to the density of the air relative to the volume of the object under consideration.

## What is conventional mass?

Air is always exerting a lifting effect on all objects. The magnitude of that effect is directly proportional to the density of the air relative to the volume of the object under consideration.

Everything we weigh is surrounded by air, so the convention for expressing the weight, or the mass of an object is basically ‘mass in air’ or Conventional Mass.

Conventional mass has the same unit as mass, because its values are defined by the multiplication of a mass by a dimensionless quantity. The unit of the quantity of conventional mass is the kilogram.

No discussion of Conventional Mass would be complete without a mention of the 8.0 g/cm3 standard. Stainless steel is the ‘standard’ material from which most high quality laboratory weights are fabricated.

Stainless steel has a density of approximately 8 g/cm3, hence the reference. Years ago, brass was the most common material used for laboratory weights, and 8.4 g/cm3 was the reference density.

The conventional mass value of a body is equal to the mass (Mc) of a standard that balances this body under conventionally chosen conditions.

The conventionally chosen conditions are:

Temperature ref = 20 °C; Density reference: ρ0 = 1.2 kg m-3; ρc = 8000 kg m-3

## Conventional Mass of an object in Calibration

The hypothetical weighing of a mass carried out in ‘perfect air’ with its distinct composition at 20 degrees Centigrade, atmospheric pressure of 760.5 mm of mercury, and a relative humidity of 50%. Under these ‘perfect conditions’, the density of air would be 1.2000 mg/cm3.

In a calibration lab the realization of these parameters is practically impossible, hence ambient conditions are stabilized to the best possible extent. Then the temperature, pressure and humidity are measured cautiously and density of the air is determined. The results of the calibration are adjusted mathematically to portray as though the calibration had been conducted in ‘perfect’ conditions.

## History of Mass and Conventional Mass Measurements

The metrological equivalence in measurement performance by various National Metrology Institutes (NMIs) is evaluated through crucial and supplementary comparisons.

These were discussed and organized by the Consultative Committees of the International Committee for Weights and Measures (CIPM) and by the Regional Metrology Organizations (RMOs).

In March 2012, the working group of mass of Inter-American Metrology System (SIM) SIM MWG7 decided to organize two supplementary comparisons including the calculation of mass and conventional mass, density and volume for E2 standard weights. This was done basically to guarantee the traceability for E2 standard weights.

## What is the relationship between mass and weight?

The mass of an object is in effect the measure of an object’s inertial property, or the amount of matter it contains.

While weight is the measure of the amount of downward force that gravity exerts on it.

The mass of an object is the amount of matter it contains, regardless of its volume or any forces acting on it.

Gravity is a force that attracts objects towards the Earth or another object. The weight of an object is defined as the force caused by gravity on that mass.

The weight of an object is a measure of the force exerted on the object by gravity, or the force that is needed to support it.

The value of mass or unit of mass that is used to identify conventional mass is the kilogram. The unit of measurement for weight is that of force, which in SI system is the Newton.

Relation between weight and mass can be defined as, an object with a mass of 1.0 kg weighs approximately 9.81 N on the surface of the Earth, which is its mass multiplied by gravity.

## True Mass v/s Conventional Mass

True mass definition: The magnitude of the difference between Conventional Mass and True Mass is the effect of air buoyancy on the difference between the volumes of the two masses.

True mass meaning: In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Scientifically, mass is the amount of matter in an object (though matter could be difficult to fathom), whereas weight is the force exerted on an object by gravity.

Conventional mass is equal to mass when the density of the object is equal to the conventional density of the reference standard of 8000 kg m-3.

## What is the value of mass?

Mass does not change with location.

To find an object’s mass by using its weight, the formula is

(M = W ÷ G) i.e., Mass equals Weight divided by the Acceleration of Gravity.

The conventional mass is defined as the mass of a material of specified density that would exactly balance an unknown object if the weighing were carried out at a temperature 20 °C in air of density 0.0012 g/cm3.

If the mass of a weight is known (e.g. from its calibration certificate) then its conventional mass can be calculated according to this definition from the following formula:

This definition shows that the conventional mass of a weight made of stainless steel which has a density close to 8000 kg / m3 deviates from its mass by only a small amount.

For other materials, the relative deviation of Mc from m ranges from about – 3 10-4 for aluminium to + 10-4 for platinum. Nevertheless, the difference between the conventional mass value of a weight and its physical mass can be significant even for weights made of stainless steel.

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