Tea, Temperature Sensors and Newton’s Law of Cooling

The Tea Dilemma

Picture the scene, you’re halfway through making a cup of tea (you’ve taken the tea bag out and you’re just about to pour the milk) when suddenly, there is a knock at the door…

You know it’s the postman (you’re clever like that) and you also know he likes to talk so you might be wrapped up in parcel-based conversation for a couple of minutes.

Naturally, you want your tea to be as hot as possible when you return and so you’re left with a dilemma – do you pour the milk first and then answer the door, or do you answer the door and then return to pour the milk?

Well today we’re going to find out with a healthy dose of science followed by an experiment video. Let’s begin!

The Theory: Newton’s Law of Cooling

Sir Isaac Newton told us through his Law of Cooling that the rate at which an object cools is proportional to the difference between its own temperature and the temperature of its surroundings.

Have no fear, this is nothing new – you already know from experience that if you put something in the freezer, it will cool faster than if you put it in the fridge. This is because the temperature difference is greater when using the freezer and therefore, the cooling is faster.

And once again for good luck, here it is in big letters:

A bigger temperature difference gives faster cooling

Okay, I think I’ve laboured that point enough… let’s move on!

Delta Tea

So what does this mean for our tea? Well, let’s consider two cups of tea:

Cup 1: The hot water is poured from the kettle and then we answer the door to the postman, leaving the tea at the initial temperature at which it was poured from the kettle. The milk is added later after we return from our parcel-based chat.

Cup 2: The hot water is poured from the kettle and then the milk is added straight away, only after this do we answer the door to the postman (the tea bag is removed too, we aren’t monsters). The addition of cold milk reduces the overall temperature of the tea so that Cup 2 is colder than Cup 1 during our conversation with┬áthe postman.

Here is an *ahem* artistic masterpiece to demonstrate the two cups:

Now just as Sir Isaac Newton told us, the cup with the greater temperature difference between itself and its surroundings will cool faster. Therefore, it should be Cup 1 which cools quicker as it is at a higher temperature than Cup 2 during the conversation.

Therefore, once we return from our chat with the postman and add the milk to Cup 1 to create two finished teas, it should be Cup 1 which is the colder of the two.

Let’s find out if this is what actually happens in reality!

The Experiment

 

Spoilers below, watch the video!

Okay, we’re clear.

Well I wasn’t expecting an observable difference in temperature, but we got one! The prediction was proved correct with Cup 1 being a whole degree and a half lower than Cup 2.

In reality, I’m pretty sure you wouldn’t be able to tell the difference between the two temperatures but you can still have a sip in the (slightly more) warm knowledge that you’ve got a whole degree and a half more to enjoy.

As a side note, I realised when I watched that back that my hand was covering the temperature read out at the moment of the big reveal… oh well, let’s hope it added to the suspense!

That’s All Folks

I hope you enjoyed this post and if you have any thoughts or questions on the topic then please leave a comment, I’d love to hear from you.

You can also pop over to the mailing list if you’d like the occasional update about happenings here at Hartley Hacks.

Stay curious!

Robin

 

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