Tea physics!!

Chancer3001

OK, random question....

If I wanted to keep a cup of tea as warm as possible, but I have to walk off for 5 minutes after putting in the water...

Question, should I add the milk before walking off or upon returning?


And why?

For arguments sake, the water in the cup is 95degrees, the milk is 4 degrees. If that helps.

Morbert

Chancer3001 wrote: »

OK, random question....

If I wanted to keep a cup of tea as warm as possible, but I have to walk off for 5 minutes after putting in the water...

Question, should I add the milk before walking off or upon returning?


And why?

For arguments sake, the water in the cup is 95degrees, the milk is 4 degrees. If that helps.

Here's a related question to help you. Which do you think would lose more heat energy in 5 minutes: A hot cup or a warm cup?

bitburger

obviously when you return, but a teabag left for that lenght will lead to a very strong cup llol

Capt'n Midnight

did someone mention tea ?

http://www.thenakedscientists.com/HTML/content/kitchenscience/exp/how-useless-is-a-chocolate-teapot/

beardedmaster

Brownian motion inducer...

Morbert

bitburger wrote: »

obviously when you returnl

That's incorrect.

Gurgle

Chancer3001 wrote: »

Question, should I add the milk before walking off or upon returning?
And why?

For arguments sake, the water in the cup is 95degrees, the milk is 4 degrees. If that helps.

Angle 1: Adding the milk increases the surface are and therefore the rate of heat loss. Put it in when you come back.

Angle 2: Adding the milk reduces the temperature and therefore the thermal gradient. Put it in before you go.

Sir Digby Chicken Caesar

buy a thermal cup

tekkit science

Capt'n Midnight

Heat transfer by conduction is

Q = UAdT

U is the heat transfer coeffient
A is area
dT is the temperature difference

so linear with respect to temperature


For radiation
Stefan's law means radiation is proportional to the fourth power of the absolute temperature

But radiation works both ways so you have to take into account that the surroundings are radiating energy back at (say) 300K


For Convection

It's complicated there is mass transfer, fluid dynamics / evaporation / condensation
- so put a lid on it :pac:

if you put the milk in now the temperature differential is lower so it will be warmer when you come back- but 95 degrees might scald the milk. Some people put the milk in first !

BTW, saw somewhere that if you work out the physics of sloshing and size of human steps then just like it's easy to get a really big wave in the bath if you keep reinforcing it then a cup of tea/coffee is almost certain to spill if you walk more than a few steps carrying one. (in other words don't take the cup with you unless you walk very slowly, have frequent stops, a lid or suspend the cup on a holder with a meter of string )

maninasia

It depends if you have left the milk out on the table and the ambient temperature. Leaving the 4C milk on the table will allow it to warm up if the surrounding temperature is warmer. If you take the milk straight out of the fridge you will have no warming effect.
Apart from this I don't see any real difference as to if you put the milk in before or after.

Chancer3001

does something 90 degrees lose heat faster in a room than something , say, 30degrees?

NIMAN

What shape is the teabag?

Arse Biscuits!

Chancer3001 wrote: »

does something 90 degrees lose heat faster in a room than something , say, 30degrees?

Simply, no, that's assuming both substances are in the same material container and that the thermal conductivity of the containers are equal and of equal volume. If both substances and container were exactly the same and the temperature of the room was perfectly distributed then the rate of heat loss would be the same.

Capt'n Midnight

Arse Biscuits! wrote: »

If both substances and container were exactly the same and the temperature of the room was perfectly distributed then the rate of heat loss would be the same.

If both substances and container were exactly the same... then the heat transfer coefficient would be the same.

And if you only consider conduction (really shiny metal) then the heat transfer rate would be proportional to their difference in temperature to the room.


If the room was 30 degrees C then something of 30 degrees would be in equilibrium , heat loss would match heat gain.

if the room was 20 degrees then the initial heat loss of the 90 degree would be 8 times that of the 30 degree

if the room was 160 degrees then the 30 degree container would have twice as much energy transferring to it as the 90 degree one

Arse Biscuits!

Capt'n Midnight wrote: »

If both substances and container were exactly the same... then the heat transfer coefficient would be the same.

And if you only consider conduction (really shiny metal) then the heat transfer rate would be proportional to their difference in temperature to the room.


If the room was 30 degrees C then something of 30 degrees would be in equilibrium , heat loss would match heat gain.

if the room was 20 degrees then the initial heat loss of the 90 degree would be 8 times that of the 30 degree

if the room was 160 degrees then the 30 degree container would have twice as much energy transferring to it as the 90 degree one

Ah... I need to study more

Capt'n Midnight

Arse Biscuits! wrote: »

Ah... I need to study more

Aristotle missed a few things too

maninasia

Basically heat loss is fairly simple to understand, as long as you dealing with the same materials. Each material or substance has it's own specific heat capacity, which affects the speed it warms or cools at. It's pretty much linear most of the time.

Milk will have a different heat capacity than water. The heat capacity of the milk will depend on what type of milk it is. There is probably a very minor effect due the difference in heat capacity of the milk and tea after mixing (due to the fat content in the milk either creating a barrier to loss of heat to the air or not) compared to the difference in heat loss/gain if the substances have not been mixed. Again it's pretty much additive and simple to calculate unless you are a NASA or semiconductor engineer whereas then it starts to get pretty darn important!

Some substances do exhibit different characteristics when changing between a solid to a gas or a liquid. Water has some very unusual properties in this regard, due to the way it freezes.

It's easier to understand heat if you think of it is as an entropic process, the heat is a measure of how energetic the molecules are. When the energy is completely lost the atoms will reach absolute zero and will be completely still. That's my simple understanding of heat.

corkgsxr

put a saucer over the top. keep the heat in. problem solved

Capt'n Midnight

maninasia wrote: »

Basically heat loss is fairly simple to understand, as long as you dealing with the same materials. Each material or substance has it's own specific heat capacity, which affects the speed it warms or cools at. It's pretty much linear most of the time.

Milk will have a different heat capacity than water. The heat capacity of the milk will depend on what type of milk it is. There is probably a very minor effect due the difference in heat capacity of the milk and tea after mixing (due to the fat content in the milk either creating a barrier to loss of heat to the air or not) compared to the difference in heat loss/gain if the substances have not been mixed. Again it's pretty much additive and simple to calculate unless you are a NASA or semiconductor engineer whereas then it starts to get pretty darn important!

Some substances do exhibit different characteristics when changing between a solid to a gas or a liquid. Water has some very unusual properties in this regard, due to the way it freezes.

It's easier to understand heat if you think of it is as an entropic process, the heat is a measure of how energetic the molecules are. When the energy is completely lost the atoms will reach absolute zero and will be completely still. That's my simple understanding of heat.

Water has a heat capacity of ~4200Kj per Kg per degree, it's a measure of how much energy it can store at a given temperature

milk isn't that far away since it's mostly water

IIRC only something like liquid ammonia has as high a heat capacity as water.


Heat transfer rate is a different thing altogether.
When fluids have an internal temperature difference you can get convection currents and the maths gets messy


Changing state from liquid to gas needs a lot of energy even though there is no temperature change, evaporative cooling and all that. Using a lid will reduce this drastically - if you want to boil water in a saucepan use a lid !

Chancer3001

someone give me the damn answer

maninasia

Just drink the damn tea already!

velosolex

maninasia wrote: »

Just drink the damn tea already!

I always leave my tea with the teabag in it for a minimum of 3 minutes prior to putting in the milk but then I only like a small quantity of same and even then still keep the teabag in as I drink. I ensure that the cup is hot first by half filling it with boiling water for at least 20 seconds, in fact prior to the automatic kettle I would invert the cup on the spout of the kettle and this gave a superheated cup, of course you could just warm it up in the microwave.

im invisible

velosolex wrote: »

...of course you could just warm it up in the microwave.

must try this, cold water, teabag, microwave, 2 minutes?

whizbang

dont't forget; by putting the milk in you have increased the volume i.e. thermal mass

Lbeard

Chancer3001 wrote: »

OK, random question....

If I wanted to keep a cup of tea as warm as possible, but I have to walk off for 5 minutes after putting in the water...

Question, should I add the milk before walking off or upon returning?

You should put the milk in before you walk away. If you wait, come back and add the milk, your tea will be colder.

And why?

The cooling of the cup of tea. Anything in a room, will eventually reach room temperature - heat doesn't flow in one direction, it flows back and forth. The room shares its' heat with the tea, the tea shares its' heat with the room. This sharing doesn't stop - but both the tea and the room will reach the same temperature.

The hotter something is, in relation to the room, the faster it cools.

But, the cooler something gets, the slower it cools - is this exponential decay.

Now if this graph appears, you'll see the exponential rate of temperature slows as two bodies of different temperature reach the same temperature.

For arguments sake, the water in the cup is 95degrees, the milk is 4 degrees. If that helps.

Let's do some science.

This is a formula used for calculating the speed of heat transfer from a hotter body to a colder one.

Rate = k•A•(T1 - T2)/d

Rate = how fast the tea is losing energy to the room
k = coefficient of heat transfer - it's a constant depending on the material.
A = is the surface area
T1 = The starting temperature of the Tea.
T2 = Room temperature.

I'm going to do some crude cheating here to simplify everything. I'm going to make A, K and d, equal to 1. (I can do this because I'm not seriously going to look up the true values).

Our formula becomes simpler; Rate = (T1 - T2), or Rate = (Ttea -Troom)

We will also say the milk drops the tea by 5 degrees, whenever you add it.

Temperature of tea without milk = 95
Temperature of tea with milk = 90
Room temperature = 20

If we put them in our formula

Rate of heat loss without milk = (95 - 20) = 75 Units of energy per second
Rate of heat loss with milk = (90 - 20) = 70 Units of energy per second

The tea without milk is losing energy/heat faster.

Now, doing the equation that would show the exponential decay in temperature. If we had all the constants, we could show precisely what temperature the tea would be at with and without milk, at five minutes.