The Numbers Game - The Cost of Energy

(Based on a presentation given by Phil Smith, mid-Sussex GP at the Sept '05 Conference)

Energy - the basic unit is the Joule (J) – roughly the energy required to lift a small apple one metre.

1 calorie = 4.186 J
1 Calorie = 1000 calories = 4.186 kJ

Power is the rate of use of energy – the basic unit is the watt (W). One watt is energy used at the rate of 1 Joule per sec.

1kW = 1000 joules per second
1kW power used for one hour takes 3600kJ
1kilowatt hour (kWh) = 3.6MJ (M=million)
1 Therm = approx 30kWh
1kWh = approx 860 Calories (860,000 calories)

Human Energy

Daily food energy = approx 2500 Calories
One man-day = about 2.9kWh
Human power rating = 121W
A loaf of bread = 1600 Calories or 1.8kWh

1 barrel oil = approx 42 US, or 35 UK, Gallons, or 159 litres.

1 litre of oil contains about 38MJ or 10.5kWh.

At $70 a barrel crude oil costs 24.5p a litre

Calorific values (kWh/kg) and costs (p/kWh) of various fuels:

As you can see most human fuels are much less energy dense and also much more expensive than the fossil fuels per kWh. This is one reason why the use of slaves for work has become uneconomic since we started using fossil fuels.

Human annual energy consumption is about 1060kWh, giving a basic running cost (if you only ate only bread) about £500 per person per year.

Some Typical machines:

• Laptop 60W at 4hrs/day costs £8.93 a year
• TV 100W at 4hrs/day costs £14.89 a year
• Vacuum Cleaner 1kW at 2hrs/week costs £10.60/year
• Kettle 2kW at 10mins/day costs £12.41 a year
• Washing Machine 1.2kWh per cycle twice a week = £12.72/year
• Fridge freezer 360kWh/year costs £36.72
• Ford Focus 1.6L 74kW for 40mins a day costs £1530 per year (or 12,000 miles at 40mpg costing £1350)
• Human slaves (2) carrying sedan chair would use 5.8kWh/day costing about £2102 per year if you fed them bread and cheese. 25 miles/day = 9000 miles/year

It is much cheaper to run a Ford Focus than a Sedan Chair to get around in ! 

NB none of the above takes account of the costs of extracting or growing the source of energy – these are significant (10:1 for food, about 1:5 for oil)

All engines are less than 100% efficient. A petrol engine is about 20% efficient; the rest is lost as heat.

But a Ford Focus weighs 1255kg, so with a driver weighing 75kg only 6% of the driving power is used to move the person. That means the overall efficiency of using a petrol car to transport a person is less than 2% - for every litre of petrol only four teaspoons full are being used to provide the energy to get the driver from A to B. The rest is wasted as heat and moving a big lump of metal and plastic around.

The human engine is about as efficient as the petrol one – around 80% of the energy from food is taken up maintaining life and given off as waste heat, around 20% can be converted into available work (muscle power).

Of course your two slaves are also carrying their own sorry souls and the sedan chair around, so you are only getting about a quarter of their output as useful work.

The other side of the coin is the CO2 produced when the fuel is burnt.

1kWh from coal produces about 0.5kg CO2
1kWh from petrol makes about 0.25kg CO2
1kWh from gas generates around 0.2kg CO2

A human generates about 900 grams CO2 per day or about 0.3kg per kWh.