How do I calculate the net mass (in Kg) of a 200 liter drum full of a liquid whose specific gravity is 1.2?

Specific gravity equals mass divided by volume:

D=M/V.

This is more or less the definition of specific gravity (or if you please, density or baricity, with quibbling differences between the terms). Here I am using D (for "density") to represent the specific gravity -- old habit.

Or to put the same equation in all 3 of its forms:

D=M/V
M=DV
V=M/D

These equations work whenever M, V are measured in units of:
- kilograms, liters
- grams, cubic centimeters
- grams, milliliters

There are many physical systems where you have three variables related like this (e.g., Ohm's Law E=IR, Poisson's Law T=P/R, and of course Newton's F=MA). The point is that given two variables, you can calculate the third by just multiplying or dividing the other two.

The only trick is figuring out whether to multiply or to divide, and if divide then which by which?

In this problem you seek mass (M) given volume (V) and specific gravity (D).

So you need an equation in the form M= which literally tells you how much "mass equals." The correct relation (from the 3 choices above) is M=DV.

So M = (1.2 Kg/L)(200 L) = (240)(Kg/L)(L) = 240 Kg

Done.

The problem asked for the "net mass" which means you forget about the mass of the container. Answer = 240 Kilograms

Notice that you multiply and divide numbers, and you "multiply and divide" units to keep everything tidy and to make sure it's "set up" right.

Once you work a bunch, it shouldn't be too tough to set it up right the first time.

Specific gravity is the density of a substance divided by the density of water. So, to get the density, multiply by the density of water (1 kg/L).

(1.2) * (1 kg/L) = (1.2 kg/L)

Since density is mass divided by volume, you just need to multiply density by volume to get mass.

(1.2 kg/lL) * (200 L) = (240 kg)

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Edit: too slow again

methos' answer is technically correct ("too slow" wins the race!) Specific gravity (SG) is treated somewhat differently than density. SG is based on water as a standard and is a "dimensionless" ratio, unlike density which has dimensions of mass divided by volume, expressed in units such as Kg/L.

But since the density of water = 1, density and SG are numerically the same. Dimensionally there is a missing "factor" of units of (Kg/L) hidden in the implied factor of 1 for the density of water.

Hope that didn't cause more confusion!

I knew that specific gravity was based on water, but I didn't realize that 1 liter of water had a mass of 1 kg. That makes the whole problem easy to understand, and solve. Thanks guys!

Note that the Celsius temperature scale is based on water, too.

Oops -- correction to my first post: LaPlace's -- not Poisson's -- Law T=PR (tension, pressure, radius of bubble or balloon). I hate being away from my personal library.

The density of water is 1000 ... not 1.

The standard system of units is MKS or SI.

rho(water) = 1000 Kg/m^3

Z80 - Because Kendor's question used liters and kilograms, it is more sensible to use the density of water in kg/L than kg/m³.

1 kg/L = 1000 kg/m³

You will arrive at the same answer either way, but if you use kg/m³, you will have to go through the extra step of converting Kendor's 200 L to m³.



On a general note, while MKS is a widely used system of units, it is not the only one. The strength of the metric system is that it can be scaled to different uses easily. We measure medicinal doses in g, not kg. We measure wavelengths of visible light in nm, not m. We measure distances traveled by car in km, not m. Different disciplines use different units and nothing is lost so long as those units are duly noted.