HEAT TRANSFERRED: FORMULAS, HOW TO CALCULATE IT AND SOLVED EXERCISES - PHYSICAL - 2024

The heat transferred is the transfer of energy between two bodies at different temperatures. The one with a higher temperature gives up heat to the one with a lower temperature. Whether a body gives up or absorbs heat, its temperature or physical state can vary depending on the mass and characteristics of the material from which it is made.

A good example is in a steaming cup of coffee. The metal spoon with which the sugar is stirred heats up. If it is left in the cup long enough, coffee and a metal spoon will end up equalizing their temperatures: the coffee will have cooled and the spoon will have given heat. Some heat will have passed into the environment, since the system is not insulated.

The coffee and the spoon come to be in thermal equilibrium after a while. Source: Pixabay.

As the temperatures become equal, thermal equilibrium has been reached.

If you did the same test with a plastic teaspoon, you would surely notice that it does not heat up as quickly as the metal one, but it will also eventually come into balance with the coffee and everything around it.

This is because metal conducts heat better than plastic. On the other hand, surely coffee yields heat at a different rate than hot chocolate or other beverage. So the heat given or absorbed by each object depends on what material or substance it is made of.

What it consists of and formulas

Heat always refers to the flow or transit of energy between one object and another, due to the difference in temperature.

That is why we speak of heat transferred or heat absorbed, since by adding or extracting heat or energy in some way, it is possible to modify the temperature of an element.

The amount of heat that the hottest object gives off is usually called Q. This value is proportional to the mass of that object. A body with a large mass is capable of giving up more heat than another with a lower mass.

Temperature difference

Another important factor in calculating heat transfer is the difference in temperature experienced by the object transferring heat. It is denoted as Δ T and is calculated as follows:

Finally, the amount of heat transferred also depends on the nature and characteristics of the object, which are quantitatively summarized in a constant called the specific heat of the material, denoted as c.

So finally the expression for the transferred heat is the following:

The act of giving in is symbolized by a negative sign.

Specific heat and heat capacity of a substance

Specific heat is the amount of heat necessary to raise the temperature of 1 g of substance by 1 ºC. It is an intrinsic property of the material. Its units in the International System are: Joule / kg. K (Joule between kilogram x temperature in degrees Kelvin).

The heat capacity C is a linked concept, but slightly different, since the mass of the object is involved. The heat capacity is defined as follows:

Its SI units are Joule / K. So the heat released can also be expressed equivalently as:

How to calculate it?

To calculate the heat transferred by an object, it is necessary to know the following:

- The specific heat of the substance that gives up heat.

- The mass of said substance

- The final temperature to be obtained

Specific heat values ​​for many materials have been determined experimentally and are available in tables.

Calorimetry

Now, if this value is not known, it is possible to obtain it with the help of a thermometer and water in a thermally insulated container: the calorimeter. A diagram of this device is shown in the figure that accompanies exercise 1.

A sample of the substance is immersed at a certain temperature in an amount of water that has previously been measured. The final temperature is measured and the specific heat of the material is determined with the values ​​obtained.

By comparing the result with the tabulated values, it can be known what substance it is. This procedure is called calorimetry.

The heat balance is carried out by conserving energy:

Q _yielded + Q _{absorbed = 0}

Solved exercises

Exercise 1

A 0.35 kg piece of copper is introduced at a temperature of 150ºC in 500 mL of water at a temperature of 25ºC. Find:

a) The final equilibrium temperature

b) How much heat flows in this process?

Data

Schematic of a basic calorimeter: an insulated container of water and a thermometer to measure changes in temperature. l Source: Dr. Tilahun Tesfaye

Solution

a) Copper gives up heat while water absorbs it. As the system is considered closed, only the water and the sample intervene in the heat balance:

On the other hand, it is required to calculate the mass of 500 mL of water:

With these data the mass of the water is calculated:

The equation for the heat in each substance is raised:

Equating the results we have:

It is a linear equation with one unknown, whose solution is:

b) The amount of heat that flows is the heat transferred or the heat absorbed:

Q _yielded = - 134.75 (32.56 - 150) J = 15823 J

Q _absorbed = 2093 (32.56 - 25) J = 15823 J

Exercise 2

A 100 g piece of copper is heated in a furnace at a temperature T _o and then placed in a 150 g copper calorimeter containing 200 g of water at 16 ° C. The final temperature once in equilibrium is 38 º C. When the calorimeter and its contents are weighed, it is found that 1.2 g of water have evaporated. What was the initial temperature T _o ?

Solution

This exercise differs from the previous one, since it must be considered that the calorimeter also absorbs heat. The heat released by the piece of copper is invested in all of the following:

- Heat the water in the calorimeter (200 g)

- Heat the copper from which the calorimeter is made (150 g)

- Evaporate 1.2 grams of water (energy is also needed for a phase change).

Thus:

- 38.5. (38 - T _o) = 22397.3

The heat needed to bring the 1.2 g of water up to 100ºC could also have been considered, but it is a fairly small amount in comparison.

References

1. Giancoli, D. 2006. Physics: Principles with Applications. 6 ^th. Ed. Prentice Hall. 400 - 410.
2. Kirkpatrick, L. 2007. Physics: A Look at the World. 6 ^ta Editing abbreviated. Cengage Learning. 156-164.
3. Rex, A. 2011. Fundamentals of Physics. Pearson. 309-332.
4. Sears, Zemansky. 2016. University Physics with Modern Physics. 14 ^th. Ed. Volume 1. 556 - 553.
5. Serway, R., Vulle, C. 2011. Fundamentals of Physics. 9 ^na Cengage Learning.