Cooking at low temperature: for how long?

The first is to produce stunningly tender food of exceptional quality and the second is to make food safe. No chef would ever desire to make their customers sick.

How do we then determine the length of time that will give us the correct result when we use low temperature to cook food?

The best tool on the market is the Polyscience 'SousVide Toolbox'. This app is available for both the iPad and iPhone. 

The thermo dynamics of food are fairly consistent, so mapping out the heating curve of food items as they come to temperature can be mathematically determined using a few basic parameters.  The PolyScience SousVide Toolbox works all of this maths out for us.  You enter in the basic information, what is to be cooked, what shape or cut is it, how thick is it, the temperature you have set the water bath to. 

It then suggests known cooking temperatures for doneness off your food item.  When you have entered the correct information in to the 'SousVide Toolbox' it not only shows you the time it will take to cook, it displays a chart showing heating and cooking times as well as decimal reduction of known pathogens and works as a countdown timer.

Reduction of known pathogens (E.coli, Listeria, Salmonella) is worked out using what is referred to as decimal reduction. 

The formula for this is simple if you have a Phd in applied mathematics, for the rest of us Douglas Baldwin has done all of the maths and set it out in charts in his essay "A practical guide to sous vide cooking". You can follow his charts or you can allow the Toolbox to work all of that out for you.