# Detailed Insights: Dimensions, Units and Conversions

Dimensions, units and conversions are essential for all chemical engineers and being able to go back and forth between different units will become second nature. It is vital for any chemical engineering student to get their head around this key concept.

## Dimensions and Units

Understanding several dimensions is the most important first step and are as follows: Mass (M), Length (L) and Time (T), Amount of substance – Mole (mole), Electric current – Ampere (A) and temperature – Kelvin (K)

Having an understanding of these basics will help a lot when coming across quantities that look difficult to be able to give dimensions to.

 Dimensions Units Length – used to locate the position of a point in space and so describe the size of a physical system Kilometre, Metre, Foot, Inch Time – conceived as a succession of events Day, Hour, Minute, Second, Nanosecond Mass – a measure of a quantity of matter Kilogram, Pound, Ton, Tonne Temperature – a measure of the energy of molecules in a system. Degree Centigrade, Celsius, Kelvin, Rankin or Fahrenheit Amount of a substance/molar amount Mole Electrical current Ampere

Below is a table of quantities, dimensions and SI units – SI units are just a modern form of the metric system used by nearly every country apart from Myanmar, Liberia and the US.

 Quantity SI units Dimensions Mass Kilogram M Length Metre L Time Second T Force Newton MLT-2 Energy Joule ML2T-2 Pressure Newton/Square metre ML-1T-2 Power Watt ML2T-3

There is no point trying to remember dimensions as there are too many and it is time-consuming, the best way to understand it to use the equations that include the quantity

an example will be used to show this:

Example 1:

As seen in the above table the dimensions of force are given, can you show how they have got there?

Force = mass x acceleration

We know that mass has dimensions of m, but what about acceleration?

Accelerations units are meters/second2

This has dimensions of length due to metres and dimensions of time due to seconds is T2 as its seconds squared.

So, the dimension of acceleration is: L/T-2

Thus, proving the dimensions of force are MLT-2:

Force = mass x acceleration

Force = M x L/T-2 = MLT-2

Example 2:

what are the dimensions of density?

The units for density are kg/m3 if you didn’t know this it’s fine you can work it out from the equation:

The equation for density is:

Density = mass/ volume

Mass is in kg and volume is in m3

The dimensions of mass we know is M, for the volume we know that volume is measured in meters (m3) and thus the dimensions would be L3.

Thus, the dimension of density is: ML-3

## Dimensional Equations

Dimensional equations are an easy way to be able to convert units and it can be done in three steps:

Step 1: Write out the given quantity and its units.

Step 2: Write in the units of conversion factors that will cancel out and replace the old units.

Step 3: Fill in the new values

Example 3:

Change the units from kg to g for 10m3/kg.

1000 g = 1 kg

10 m3kg x (1kg1000 g) = 0.01 m3g

Hint: Always be careful about how you cancel your units and the best is to write it out, so you don’t make unnecessary mistakes.

## What do you think? ### An In Depth Guide To Basic Reaction Kinetics 