# Cooling of Cup of Tea

## Homework Statement

Hi people, Im just having a little play with some physics because basically I went to drink my tea this morning and its always too hot. Then I wait and its always too cold. So therefore I fancy to try and workout how long should I leave it until it is cool. I found a study that says 60 deg c is 'perfect'. Therefore for my size of mug I want to know how long I should leave it in the morning.

My tea' consists of the ceramic mug, water, and milk. Obviously the tea bag will absorb some heat but I can't be bothered with that.

I assume that heat will be lost through conduction with the air at the sides of mug, convection from the top and also radiation (can I assume black body?).

What would be a good way of going about this? I assume newtons law of cooling is the way forward but I haven't done it for a long time.

I fancy going reasonably accurately with this so just need to check my line of thinking

## Homework Equations

+ Info[/B]

Specific Heat Capacity of Ceramic
SHP of Water
SHC of Milk
Newtons Law of Cooling

I know the dimensions of my mug

## The Attempt at a Solution

No attempt, I don't wish to have an answer just some ideas that I can look into so I can go away and work some stuff out. [/B]

Doug Huffman
Gold Member
Discover time to temperature empirically, with a watch and thermometer. The conditions of my coffee brewing vary very little.

Bystander
Homework Helper
Gold Member
Latent heat losses from evaporation.

CWatters
Homework Helper
Gold Member
The simplest way is to put a thermometer in your cup an time how long it takes to fall to 60C.

Quite hard to calculate. Even working out the starting temperature is involved. For example you have:

Boiling water at 100C
Coffee cup at room temperature
Milk at perhaps 3C

To work out the starting temperature you would need the mass, specific heat capacity and temperature of all three. Then you might have to make an assumption that when all three are in contact with each other they all reach the same equilibrium temperature which might not be the case in reality.

The28
Doug Huffman
Gold Member
LOL That's just what was done in the cited paper, the bulk of the paper was an attempt to model the practical information.