A lot of huffing and puffing

By Marcus Wilson 15/04/2015


While there is some great fiction out there, one really shouldn't try to learn much physics from it. One case in point, which I am forced to listen to over and over by the youngest member of our house, is the story of the Three Little Pigs. 

I'm not talking here about the relative merits of various building materials for construction of houses. Straw, wood and brick all have their place. I refer to the rather rapid boiling of the pot of water that the Third Little Pig puts on the fire when the wolf comes knocking at the door. 

In the version of the story that we have on CD, thw wolf, fresh from his succesful huffing- and puffing- of the straw and wood houses, arrives at the home of the Third Little Pig, where  the First and Second Little Pigs have taken refuge. A house made of brick. The door is locked in his face. No problem for the wolf – or so he thinks. A little more huff and puff and this one will be blown in to.  But this time he's mistaken. The house stands still. The angry wolf now resorts to plan B. He puts safety regulations aside and climbs onto the roof of the house, with the intention of gaining ingress via the chimney. 

Time for the third Little Pig to move quickly. He gets a fire going, puts a wolf-sized  pot of water on in, and gets it boiling – just in time, as the wolf drops down the chimney. This version of the story ends with the wolf fleeing in pain (rather than cooked) and the Three Little Pigs jubilant. 

Actually, the story doesn't end, because Benjamin now pushes the button on the CD player to play it again. And again…

Now, just how much power does the Third Little Pig have at his disposal to boil a wolf-sized pot of water in the time taken for a wolf to climb up onto the roof and head down the chimney. The wolf is in a foul mood, so he's not going to hang around. Let's say it's going to take him  minute for this task. A wolf-sized pot might be around 100 litres in size. If it's full of water at about room temperature, this 100 litres of water has to gain 75 degrees Celsius in just 60 seconds. 

One litre of water takes 4200 joules of energy to raise its temperature by 1 degree C. That's called the 'specific heat capacity'. To raise 100 litres by 75 degrees, we therefore need 4200 times 100 times 75 = 31 500 000 joules. This happens in sixty seconds – thats about half a million joules per second. 

What does that mean? One joule per second is one watt of power. So here we have about 500 kW of power – a kW (kilowatt) being a thousand watts.  

This is something pretty substantial. If you've watched the disc on your electricity meter spin around, you'll know that it's rotation rate is a measure of your power consumption. Usually 200 revolutions equals 1 kWh of energy. Do the maths and you'll find that 1 revolution per second (a seriously high domestic consumption) equates to 18 kW of power.  500 kW equates to about 30 revolutions per second. Dizzy stuff.  

If the Little Pigs were relying on electricity they'd be needing to upgrade their mains connection. But they are using wood. Consumer NZ tells me that efficient, domestic wood-pellet fires can produce about 10 kW of power. To hit the 500 kW range, the pigs obviously have a sizeable one indeed.