# Proof , Newtond law of cooling

• nithin
In summary, during a practical on thermodynamics, the question of whether the rate of heat loss for two different liquids, oil and water, placed in identical calorimetry copper cups would be the same. The reasoning was that the copper cups have a fixed amount of power and the dimensions are constant, leading to the same rate of heat loss. Additionally, Newton's law of cooling was discussed, stating that the rate of change in temperature is proportional to the difference in temperature between the object and the ambient temperature. This can be represented by the equation rate of change in temperature = -k(T - Troom), where k is a constant unique to each object. Therefore, the rate of energy loss may be the same, but since the specific heat
nithin
Ok hi guys,
recently i was doing a practical on thermodynamics. Then i came across of a question which was to comment on the assumption that the rate of heat loss for 2 different liquids , placed in identical calorimetry copper cups was the same.( the 2 liquids started off at the same temperature ( the liquids were oil and water)).

Ok my reasoning for the rate of heat loss being the same was that the copper cup,can only have a loss in energy at a fixed amount of power as the dimensions of the cup are kept constant. Please correct me if i am wrong.

Then i also commented on Newtons law of cooling( rate of change of temperature is proportional to the difference in temperature between the objects temperature and the ambient temperature) If it were to be written in a equation,it would be the (rate of change in temperature = -k(T - Troom) . Okay the k here is a constant which is different for every object.My reasoning is that to bring down the temperature of 2 different objects by a kelvin would require different amounts of energy as the the specific heat capacity of every object is unique. Furthermore the rate of energy loss is the same,hence 2 different objects would not have the same k value.Asthey would require different amounts of time to cool down. Please comment on these satements

Assuming I understand your reasoning, you are correct: the rate of heat transfer for any given temperature is the same, but since the specific heats are different, the rates of temperature change are different.

Thank you!

## 1. What is the proof for Newton's law of cooling?

The proof for Newton's law of cooling is based on the principle of heat transfer. It states that the rate of heat loss (or gain) of an object is directly proportional to the difference in temperature between the object and its surroundings. This can be represented mathematically as dQ/dt = hA(T-Ts), where dQ/dt is the rate of heat transfer, h is the heat transfer coefficient, A is the surface area of the object, T is the temperature of the object, and Ts is the temperature of the surroundings.

## 2. How does Newton's law of cooling apply to real life situations?

Newton's law of cooling can be observed in various real life situations such as the cooling of a hot beverage, the process of sweating to cool down the body, or the use of cooling fans or air conditioning systems. It is also used in industries for processes such as food preservation and refrigeration.

## 3. Can Newton's law of cooling be used to predict the temperature of an object at a specific time?

Yes, Newton's law of cooling can be used to predict the temperature of an object at a specific time as long as the initial temperature of the object, the temperature of the surroundings, and the heat transfer coefficient are known. This is often used in engineering and physics applications to determine the rate of cooling or heating of an object.

## 4. What factors affect the rate of cooling according to Newton's law of cooling?

The rate of cooling according to Newton's law of cooling is affected by factors such as the temperature difference between the object and its surroundings, the surface area of the object, and the heat transfer coefficient. Other factors such as the material of the object, its shape, and the density of the surrounding medium can also have an impact.

## 5. Are there any limitations to Newton's law of cooling?

Yes, there are some limitations to Newton's law of cooling. It assumes that the temperature of the surroundings remains constant, which may not always be the case. It also assumes that the object is well-insulated and that the heat transfer coefficient remains constant. In reality, these factors may vary and affect the accuracy of the predicted temperature. Additionally, this law is only applicable to objects that are undergoing convective heat transfer.

• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
14
Views
970
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
724
• Introductory Physics Homework Help
Replies
7
Views
879
• Introductory Physics Homework Help
Replies
1
Views
924
• Introductory Physics Homework Help
Replies
16
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
894
• Classical Physics
Replies
1
Views
506