Experts maths formula for brewing perfect cup of tea – including how to stir

For tea lovers, the whizzes at the institute of mathematics have figured out the way to make the perfect cup of tea – and all it takes is a mathematical formula.

We in Britain love drinking tea. With more than one hundred million cups of tea brewed every day, it's fitting that we should learn to make it properly.

But according to the institute of mathematics, the secret ingredient isn't putting the milk in before the tea and hot water (but we knew that already), or adding an extra half teaspoon of sugar – it is in facts maths.

While the formula is pretty complex, the Mirror helps break it down well.

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Basically, there is a general formula that stands for pretty much everything you can think of. It’s known as the 'conversion of mass equation’ which basically stands for:

‘The change in density of some stuff in someplace is equal to the amount of stuff coming in to said place minus the amount of stuff going out of said place.’

Bear with us here, because it does get a little simpler. To make this a little more mathematical, the Institute of Mathematics used a spatial variable with a temporal variable and considered something known as an arbitrary volume.

Long story short, this equation can refer to pretty much anything, whether that be zombies, diseases, chemicals – even the perfect brew.

How to stir your cuppa

Let’s be honest, you’re going to want your cuppa evenly distributed. There’s nothing worse than being given a cup of tea that hasn’t been stirred properly, or even worse, been stirred too quickly so there’s all weird bubbles on it.

In the maths world, the two steps involved in making your cuppa are letting your tea seep out of its bag (which is known as an uncontrollable random movement) and the second is advection. This is known as transport with the mixture velocity (how much you stir it.)

We’ve written down the three equations behind stirring your tea perfectly, prepare to have your mind blown.

The first equation is: J = — D ▽ ρ + ρ v

In this case, the ‘D’ stands for the diffusion, which you are then adding to the ‘PV’ which is the advection (the act of stirring the tea.)

After much complex research, The Institute of Mathematics found that the ‘advection’ will dominate the ‘diffusion’ when it comes to mixing your tea.

Long story short is that mixing will only be done quickly if you mix it hard enough, and that makes a better brew, so don't mess about it.

What about the temperature?

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Some like it lukewarm so they can sip it, others prepare it piping hot so it almost burns their tongue.

But what exactly, according to maths, is the perfect temperature for a brew? Let’s take a look.

There are a few things that need to be taken into consideration here, and that’s the size of the mug, the material of the mug and the heat of the water from the kettle.

To consider all of this, they focus on ‘Newton’s law of cooling’ to estimate a change in temperature.

We can actually use Newton’s law of cooling to estimate the change in temperature of the entirety of the tea, without considering the spatial variation. Solving the equation as an ordinary differential equation gives:

T(t) = T1 + Ae-ct,

This means that as a whole, the cooling coefficient of tea is quite small; an approximation of c = 0.0005 should be fine for most mugs. Pretty cool, right?

For those who like to drink their tea at a specific temperature and are wondering how long they need to wait until they can have a sip, there’s an equation for that too:

T = 20001n (80)

(T2 – 293.15)

In this equation, you’ll need to know your ideal cup of tea temperature, square that, which will tell you how many minutes.

Is your brain hurting yet? Maybe you should go and make yourself the perfect cuppa?

For those who think they already make the perfect brew, these equations will definitely put your skills to the test, just make sure you pop to the shop to get some biscuits.

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