# What is the Ideal Temperature for Cooling a Cup of Tea?

• The28
In summary, the conversation is about trying to figure out how long to leave a mug of tea to cool down to the perfect temperature of 60 degrees Celsius. The person mentions factors such as the materials of the mug and the tea, as well as heat loss through conduction, convection, and radiation. They also mention using Newton's Law of Cooling but are unsure about the calculations involved. Suggestions are made to time the cooling process empirically with a thermometer, or to use a paper with a model for practical information.

## Homework Statement

Hi people, I am 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]

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

Latent heat losses from evaporation.

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

## 1. How does a cup of tea cool down?

When a cup of tea is left to cool, it loses heat to its surroundings through a process called convection. This means that the hot tea molecules transfer their energy to the cooler air molecules around them, causing the tea to gradually reach room temperature.

## 2. Why does a cup of tea cool faster when stirred?

Stirring a cup of tea helps to distribute the hot liquid, exposing more of it to the cooler air and increasing the rate of heat transfer. This leads to a faster cooling process compared to leaving the tea unstirred.

## 3. How does the material of the cup affect the rate of cooling?

The material of the cup can affect the rate of cooling by providing insulation. For example, a ceramic or glass cup will retain heat better than a metal cup, slowing down the cooling process. However, a metal cup will transfer heat more quickly, causing the tea to cool faster.

## 4. Does the size of the cup affect how quickly the tea cools?

Yes, the size of the cup can affect the rate of cooling. A larger cup will have more surface area, allowing for more heat to be lost to the air. This means that a larger cup will cool faster than a smaller cup.

## 5. Can adding milk or cream to tea affect the cooling process?

Adding milk or cream to tea can slightly affect the cooling process due to its density. The addition of milk or cream can help to insulate the tea, slowing down the cooling process. However, the difference in cooling time is minimal and may not be noticeable to the average person.