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Blog: What's in a number?
How our lives are dominated by numbers yet we somehow get it wrong

6. What is the cost of ice?

You can buy ice in the supermarket in Britain for about 65p/kg. It's a bit of a lazy way to get it, so let's just calculate how much it costs to make. suppose you start from tap water at 15 C and freeze it. Then you need to cool the water first to 0 C and then you need to take more heat out of the water to freeze it. The first component requires a cooling of 4180 x 15 J, where 4180 is the specific heat capacity of water and 15 is the temperature decrease. This comes to 62.7 kJ. The freezing part of the exercise requires heat loss of 333.55 kJ/kg (the latent heat of fusion of water), giving a total cooling of about 396 kJ/kg.

We need also to consider that the freezer cannot be 100% efficient, far from it, as you are having to do extra work to decrease the heat content of the water. We can assume a factor of 3 for the total work. In other words, each kilogramme of water at 15 C requires about 1200 kJ to freeze.

Taking account that 1 unit of electricity is 1 kWh = 3600 kJ, 1 kg of water takes about one third of a unit of electricity. At typical UK prices of 15p per unit, the cost of freezing water at home works out then at about 5p/kg.

The supermarket mark-up of a factor of 13 is therefore enormous. Taking account of additional costs associated with making the ice: bagging it in convenient amounts, maintaining it at low temperatures, and transporting it to the retail locations, the cost of the ice probably doubles to 10p/kg. It's still way below the retail price of 65p.

Anyone who cares about the environment should not be buying ready-made ice. It is easy to make at home and requires very little of the additional costs associated with the retail product, i.e. bagging and transport. Maintenance costs, small though they are, will be even smaller if you make just the ice you need.

Bottled water --- for which similarly the retail price is considerably higher than the production cost --- has been rightly condemned as an environmental disgrace. UK industry is also, according to the Department of Environment, Food and Rural Affairs, selling ice to Sweden. The Swedes should know better. I think it is time that ready-made ice is condemned in the same way as bottled water.

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