Named Derived Units

Introduction

Some derived units become long and awkward when written in base units. The unit of energy, for instance, is kg m² s⁻². Writing that every time would be tiresome, so the SI gives such frequently used units their own names, usually honouring a scientist. In chemistry four of these appear constantly: the newton , the pascal , the joule and the watt . Each is still built from base units — the name is simply a shorthand.

Core explanation

Each named unit comes from a defining equation, and each one builds on the last.

Newton (N) — force. Force = mass × acceleration. Acceleration is measured in m s⁻², so the unit of force is kg × m s⁻² = kg m s⁻². This is called the newton : 1 N is the force needed to give a 1 kg mass an acceleration of 1 m s⁻². An apple of about 100 g weighs roughly 1 N on Earth.

Pascal (Pa) — pressure. Pressure = force ÷ area, so its unit is N ÷ m² = N m⁻². This is the pascal . One pascal is a very small pressure — roughly that of a sheet of paper resting on a table. Atmospheric pressure at sea level is about 101 000 Pa, so chemists usually write it as about 101 kPa (kilopascals). Pressure matters wherever gases are involved, such as in gas volumes and reaction rates.

Joule (J) — energy. Work done = force × distance, so energy has the unit N × m = N m, called the joule . One joule is about the energy needed to lift a 100 g apple through 1 m. In base units, 1 J = 1 kg m² s⁻². Energy changes in chemical reactions are usually quoted in kJ mol⁻¹ because single joules are tiny on a chemical scale.

Watt (W) — power. Power is the rate of transferring energy: power = energy ÷ time, so its unit is J ÷ s = J s⁻¹, called the watt . A 60 W lamp transfers 60 joules every second. An electric kettle is typically rated at 2000–3000 W.

Unit Symbol Quantity In other units In base units --- --- --- --- --- newton N force — kg m s⁻² pascal Pa pressure N m⁻² kg m⁻¹ s⁻² joule J energy N m kg m² s⁻² watt W power J s⁻¹ kg m² s⁻³

Writing the names. When written in full, unit names take a lower-case letter (newton, pascal) even though they honour people (Newton, Pascal). The symbols of units named after people take a capital letter: N, Pa, J, W.

Formulae

force = mass × acceleration → 1 N = 1 kg m s⁻²

pressure = force ÷ area → 1 Pa = 1 N m⁻²

energy (work) = force × distance → 1 J = 1 N m

power = energy ÷ time → 1 W = 1 J s⁻¹

Step-by-step reasoning

To express a named unit in base units:

1. Write its defining equation, for example pressure = force ÷ area. 2. Replace each quantity by its unit: N ÷ m². 3. Replace any named unit by its base-unit form: (kg m s⁻²) ÷ m². 4. Combine the powers of each base unit: kg m¹⁻² s⁻² = kg m⁻¹ s⁻².

Visual explanation

Picture a staircase of four steps. The bottom step holds the base units kg, m and s. The next step up is the newton, built from them. The pascal and joule each stand on the newton (dividing by area or multiplying by distance), and the watt stands on the joule, dividing by time.

Real-world analogy

A named unit is like a nickname. "Kilogram metre per second squared" is the full formal name; "newton" is what everyone calls it day to day. The person is the same whichever name you use, just as the unit is the same whether it is written N or kg m s⁻².

Real-world example

Food labels in the UK and Europe give energy in kilojoules as well as kilocalories. A typical 30 g bowl of breakfast cereal provides roughly 450 kJ. The chemistry of respiration releases this energy in your cells, and the joule links that biology directly to the physics of work and heat.

Why?

Why give units special names at all? Names make equations easier to read and reduce errors. Writing "101 kPa" is quicker and clearer than "101 000 kg m⁻¹ s⁻²", yet because the name is defined from base units, nothing is lost: any calculation can still be checked by expanding back into kg, m and s.

Common misconception

"Watts and joules measure the same thing." A joule is an amount of energy; a watt is a rate — joules per second. A 2000 W kettle running for 60 s transfers 2000 × 60 = 120 000 J. Confusing the two is like confusing distance with speed.

Worked example

Question: A force of 50 N presses evenly on an area of 0.25 m². What pressure does it exert, in Pa and in kPa?

Reasoning: pressure = force ÷ area = 50 N ÷ 0.25 m² = 200 N m⁻² = 200 Pa. Since 1 kPa = 1000 Pa, this is 200 ÷ 1000 = 0.20 kPa.

Answer: 200 Pa, which is 0.20 kPa.

Quick check

1. Which named unit is equal to one joule per second? Answer: The watt (W).

Exam focus

Learn the four definitions as equations: N = kg m s⁻², Pa = N m⁻², J = N m and W = J s⁻¹. Questions often ask you to show a unit in base units, so practise the step of replacing named units and collecting indices. Use capital letters for the symbols but lower case for the full names.

Advanced insight

The SI has 22 named derived units in total, including the coulomb (charge, A s), the volt (J C⁻¹), the hertz (s⁻¹) and the degree Celsius. Remarkably, every one of them can be written as a product of powers of the seven base units, which is what makes the SI "coherent": no numerical factors other than 1 appear when base units combine.

Summary

The newton (force, kg m s⁻²), pascal (pressure, N m⁻²), joule (energy, N m) and watt (power, J s⁻¹) are named derived units. Each comes from a defining equation and can be expanded into base units. Names are lower case, symbols are capitals. In chemistry, pressures are usually given in kPa and energies in kJ.

Practice questions

1. State the SI unit and symbol for energy and for pressure. Answer: Energy: the joule, J. Pressure: the pascal, Pa. 2. Show that the joule can be written as kg m² s⁻². Answer: 1 J = 1 N m, and 1 N = 1 kg m s⁻², so 1 J = kg m s⁻² × m = kg m² s⁻². 3. A lamp transfers 1800 J of energy in 30 s. What is its power? Answer: power = energy ÷ time = 1800 J ÷ 30 s = 60 W. 4. Standard atmospheric pressure is about 101 000 Pa. Express this in kPa. Answer: 101 000 ÷ 1000 = 101 kPa.