SPECIFIC HEAT: WHAT IT CONSISTS OF, HOW IT IS CALCULATED AND EXAMPLES - CHEMISTRY - 2024

The specific heat is the quantity of energy to be absorbed one gram of a substance to increase its temperature by one degree Celsius. It is an intensive physical property, since it does not depend on mass as it is expressed only for one gram of substance; however, it is related to the number of particles and their molar mass, as well as the intermolecular forces that bind them.

The amount of energy absorbed by the substance is expressed in units of joule (J), and less commonly, in calories (Cal). Generally, it is assumed that energy is absorbed through heat; however, the energy can come from another source, such as work done on the substance (rigorous stirring, for example).

Boiling water. Source: Pixabay

The image above shows a kettle from which the water vapors generated by its heating are released. To heat the water, it must absorb heat from the flame located under the kettle. Thus, as time passes, and depending on the intensity of the fire, the water will boil when it reaches its boiling point.

Specific heat establishes how much energy water consumes for each degree ºC that its temperature increases. This value is constant if different volumes of water are heated in the same kettle, since as said at the beginning, it is an intensive property.

What does vary is the total amount of energy absorbed by each mass of heated water, also known as the heat capacity. The larger the mass of water to be heated (2, 4, 10, 20 liters), the greater its heat capacity; but its specific heat remains the same.

This property depends on the pressure, temperature and volume; however, for the sake of simple understanding, their corresponding variations are omitted.

What is specific heat?

What specific heat meant for a given substance was defined. However, its true meaning is better expressed with its formula, which makes it clear through its units which are the clearances it involves when the variables on which it depends are analyzed. Its formula is:

Ce = Q / ΔT m

Where Q is the absorbed heat, ΔT the change in temperature, and m is the mass of the substance; that according to the definition corresponds to a gram. Doing an analysis of its units we have:

Ce = J / ºC · g

Which can also be expressed in the following ways:

Ce = kJ / K g

Ce = J / ºC · Kg

The first of them is the simplest, and it is with which the examples will be approached in the following sections.

The formula explicitly indicates the amount of energy absorbed (J) by one gram of substance in one degree ºC. If we wanted to clear this amount of energy, we would have to leave the equation J aside:

J = Ce · ºC · g

That expressed in a more appropriate way and according to the variables would be:

Q = Ce ΔT m

How is specific heat calculated?

Water as a reference

In the above formula, 'm' does not represent a gram of substance, since it is already implicitly found in Ce. This formula is very useful to calculate the specific heats of various substances through calorimetry.

How? Using the definition of calories, which is the amount of energy needed to heat a gram of water from 14.5 to 15.5ºC; this is equal to 4,184 J.

The specific heat of water is abnormally high, and this property is used to measure the specific heats of other substances knowing the value of 4.184 J.

What does it mean for a specific heat to be high? That it offers considerable resistance to increase its temperature, so it must absorb more energy; that is, water needs to be heated for much longer compared to other substances, which in the vicinity of a heat source heat up almost instantly.

For this reason, water is used in calorimetric measurements, since it does not experience sudden changes in temperature when absorbing the energy released from chemical reactions; or, for this case, from contact with another hotter material.

Thermal equilibrium

Since water needs to absorb a lot of heat to increase its temperature, the heat can come from a hot metal, for example. Taking into account the masses of water and metal, a heat exchange will occur between them until what is called thermal equilibrium is reached.

When this occurs, the temperatures of the water and the metal equalize. The heat given off by hot metal is equal to that absorbed by water.

Mathematical development

Knowing this, and with the last formula for Q just described, we have:

Q _Water = -Q _Metal

The negative sign indicates that heat is released from the warmer body (metal) to the cooler body (water). Each substance has its own specific heat Ce, and its mass, so this expression must be developed as follows:

Q _Water = Ce _Water · ΔT _Water · m _Water = - (Ce _Metal · ΔT _Metal · m _Metal)

The unknown is Ce _Metal, since in thermal equilibrium the final temperature for both water and metal is the same; in addition, the initial temperatures of the water and the metal are known before contacting, as well as their masses. Therefore, Ce _Metal must be cleared:

Ce _Metal = (Ce _Water · ΔT _Water · m _Water) / (-ΔT _Metal · m _Metal)

Without forgetting that Ce _Water is 4.184 J / ºC · g. If ΔT _Water and ΔT _Metal are developed, we will have (T _f - T _Water) and (T _f - T _Metal), respectively. The water heats up, while the metal cools, and that is why the negative sign multiplies ΔT _Metal, leaving (T _Metal - T _f). Otherwise, ΔT _Metal would have a negative value because it is T _f smaller (colder) than T _Metal.

The equation is then finally expressed in this way:

Ce _Metal = Ce _Water · (T _f - T _Water) · m _Water / (T _Metal - T _f) · m _Metal

And with it the specific heats are calculated.

Calculation example

There is a sphere of a strange metal that weighs 130g, and has a temperature of 90ºC. This is immersed in a 100g container of water at 25ºC, inside a calorimeter. Upon reaching thermal equilibrium, the temperature of the container becomes 40 ° C. Calculate the Ce of the metal.

The final temperature, T _f, is 40 ° C. Knowing the other data, Ce can then be determined directly:

Ce _Metal = (4,184 J / ºC · g · (40 - 25) ºC · 100g) / (90 - 40) ºC · 130g

Ce _Metal = 0.965 J / ºC · g

Note that the specific heat of water is about four times that of metal (4.184 / 0.965).

When Ce is very small, the greater its tendency to heat up; which is related to its thermal conductivity and diffusion. A metal with a higher Ce will tend to release or lose more heat, when it comes into contact with another material, compared to another metal with a lower Ce.

Examples

Specific heats for different substances are shown below.

Water

The specific heat of water, as stated, is 4.184 J / ° C · g.

Thanks to this value, it can get a lot of sun in the ocean and the water will hardly evaporate to an appreciable degree. This results in a thermal difference that does not affect marine life. For example, when you go to the beach to swim, even if it is very sunny outside, the water feels a lower, cooler temperature.

Hot water also needs to release a lot of energy to cool itself. In the process, it heats the circulating air masses, raising (temperate) temperatures somewhat in coastal regions during winters.

Another interesting example is that if we weren't made of water, a day in the sun could be deadly, because our body temperatures would rise rapidly.

This unique value of Ce is due to intermolecular hydrogen bonds. These absorb heat to break down, so they store energy. Until they are broken, the water molecules will not be able to vibrate increasing the average kinetic energy, which is reflected in an increase in temperature.

Ice

The specific heat of ice is 2,090 J / ºC · g. Like that of water, it has an unusually high value. This means that an iceberg, for example, would need to absorb an enormous amount of heat to increase its temperature. However, some icebergs today have even absorbed the heat needed to melt (latent heat of fusion).

Aluminum

The specific heat of aluminum is 0.900 J / ºC · g. It is slightly lower than that of the metal in the sphere (0.965 J / ºC · g). Here the heat is absorbed to vibrate the metal atoms of aluminum in their crystalline structures, and not individual molecules held together by intermolecular forces.

Iron

The specific heat of iron is 0.444 J / ºC · g. Being less than aluminum, it means that it offers less resistance when heated; that is, before a fire a piece of iron will turn red hot much earlier than a piece of aluminum.

Aluminum being more resistant to heating, keeps food hot longer when the famous aluminum foil is used to wrap snacks.

Air

The specific heat of air is approximately 1.003 J / ºC · g. This value is highly subject to pressures and temperatures because it consists of a gaseous mixture. Here the heat is absorbed to vibrate the molecules of nitrogen, oxygen, carbon dioxide, argon, etc.

Silver

Finally, the specific heat for silver is 0.234 J / ºC · g. Of all the substances mentioned, it has the lowest Ce value. This means that when faced with iron and aluminum, a piece of silver would heat up much more at the same time than the other two metals. In fact, it harmonizes with its high thermal conductivity.

References

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