SENSITIVE HEAT: CONCEPT, FORMULAS AND SOLVED EXERCISES - PHYSICAL - 2024

The sensible heat is the thermal energy supplied to an object by its temperature to rise. It is the opposite of latent heat, in which thermal energy does not increase the temperature but promotes a phase change, for example from solid to liquid.

An example clarifies the concept. Suppose we have a pot of water at room temperature of 20 ° C. When we place it on the stove, the supplied heat increases the temperature of the water slowly until it reaches 100 ° C (boiling temperature of water at sea level). The supplied heat is called sensible heat.

The heat that warms the hands is sensible heat. Source: Pixabay

Once the water reaches the boiling point, the heat supplied by the burner no longer raises the temperature of the water, which remains at 100 ° C. In this case the thermal energy supplied is invested in evaporating the water. The supplied heat is latent because it did not raise the temperature, but instead caused a change from the liquid phase to the gas phase.

It is an experimental fact that the sensible heat necessary to achieve a certain variation in temperature is directly proportional to that variation and to the mass of the object.

Concept and formulas

It has been observed that apart from the mass and the temperature difference, sensible heat also depends on the material. For this reason, the constant of proportionality between sensible heat and the product of mass and temperature difference is called specific heat.

The amount of sensible heat supplied also depends on how the process is carried out. For example, it is different if the process is carried out at constant volume than at constant pressure.

The formula for sensible heat in an isobaric process, that is to say at constant pressure, is the following:

Q = cp. m (T f - T i)

In the above equation Q is the sensible heat supplied to the object of mass m, which has raised its initial temperature T _i to the final value Tf. In the previous equation also appears cp, which is the specific heat of the material at constant pressure because the process has been carried out in this way.

Note also that sensible heat is positive when it is absorbed by the object and causes a rise in temperature.

In the case that heat is supplied to a gas enclosed in a rigid container, the process will be isochoric, that is, at constant volume; and the sensible heat formula will be written like this:

Q = c v. m. (T f - T i)

The adiabatic coefficient γ

The quotient between the specific heat at constant pressure and the specific heat at constant volume for the same material or substance is called the adiabatic coefficient, which is generally denoted by the Greek letter gamma γ.

The adiabatic coefficient is greater than unity. The heat required to raise the temperature of a one-gram body by one degree is greater in an isobaric process than in an isochoric one.

This is because in the first case part of the heat is used to carry out mechanical work.

In addition to specific heat, the heat capacity of a body is also usually defined. This is the amount of heat necessary to raise the temperature of that body one degree centigrade.

Heat capacity C

Heat capacity is denoted by a capital C, while specific heat by a small c. The relationship between both quantities is:

C = c⋅ m

Where m is the mass of the body.

Molar specific heat is also used, which is defined as the amount of sensible heat necessary to raise a temperature of one mole of substance by one degree Celsius or Kelvin.

Specific heat in solids, liquids and gases

The molar specific heat of most solids has a value close to 3 times R, where R is the universal gas constant. R = 8.314472 J / (mol *).

For example, aluminum has molar specific heat 24.2 J / (mol ℃), copper 24.5 J / (mol ℃), gold 25.4 J / (mol ℃), and soft iron 25.1 J / (mol ℃). Note that these values ​​are close to 3R = 24.9 J / (mol ℃).

In contrast, for most gases the molar specific heat is close to n (R / 2), where n is an integer and R is the universal gas constant. The integer n is related to the number of degrees of freedom of the molecule that makes up the gas.

For example, in a monatomic ideal gas, whose molecule only has the three translational degrees of freedom, the molar specific heat at constant volume is 3 (R / 2). But if it is a diatomic ideal gas, there are additionally two rotational degrees, so cv = 5 (R / 2).

In ideal gases, the following relationship between molar specific heat at constant pressure and constant volume holds: cp = cv + R.

The water deserves a special mention. In a liquid state at 25 ℃, water has cp = 4.1813 J / (g ℃), water vapor at 100 degrees Celsius has cp = 2.080 J / (g ℃) and water ice at zero degrees Celsius has cp = 2,050 J / (g *).

Difference with latent heat

Matter can be in three states: solid, liquid, and gas. Energy is required to change state, but each substance responds to it in a different way according to its molecular and atomic characteristics.

When a solid is melting or a liquid is evaporating, the temperature of the object remains constant until all the particles have changed their state.

For this reason, it is possible that a substance is in equilibrium in two phases: solid - liquid or liquid - vapor, for example. A quantity of the substance can be transferred from one state to another by adding or removing a little heat, while the temperature remains fixed.

The heat supplied to a material causes its particles to vibrate faster and increase their kinetic energy. This translates into a rise in temperature.

It is possible that the energy they acquire is so great that they no longer return to their equilibrium position and the separation between them increases. When this happens the temperature does not increase, but the substance goes from solid to liquid or from liquid to gas.

The heat required for this to happen is known as latent heat. Therefore, latent heat is the heat by which a substance can change phase.

Here is the difference with sensible heat. A substance that absorbs sensible heat increases its temperature and remains in the same state.

How to calculate latent heat?

Latent heat is calculated by the equation:

Where L can be the specific heat of vaporization or the heat of fusion. The units of L are energy / mass.

Scientists have given heat numerous names, depending on the type of reaction in which it participates. For example, there is the heat of reaction, the heat of combustion, the heat of solidification, the heat of solution, the heat of sublimation, and many others.

The values ​​of many of these types of heat for different substances are tabulated.

Solved exercises

Example 1

Suppose a that has a piece of aluminum of mass 3 kg. Initially it is at 20 ° C and you want to raise its temperature to 100 ° C. Calculate the sensible heat required.

Solution

First we need to know the specific heat of aluminum

cp = 0.897 J / (g ° C)

Then the amount of heat needed to heat the piece of aluminum will be

Q = cpm (Tf - Ti) = 0.897 * 3000 * (100 - 20) J

Q = 215 280 J

Example 2

Calculate the amount of heat required to heat 1 liter of water from 25 ° C to 100 ° C at sea level. Express the result also in kilocalories.

Solution

The first thing to remember is that 1 liter of water weighs 1 kg, that is, 1000 grams.

Q = cpm (Tf - Ti) = 4.1813 J / (g ℃) * 1000 g * (100 ℃ - 25 ℃) = 313597.5 J

The calorie is a unit of energy that is defined as the sensible heat necessary to raise a gram of water by one degree Celsius. Therefore, 1 calorie equals 4.1813 Joules.

Q = 313597.5 J * (1 cal / 4.1813 J) = 75000 cal = 75 kcal.

Example 3

A 360.16 gram piece of material is heated from 37 ℃ to 140 ℃. The thermal energy supplied is 1150 calories.

Heating the sample. Source: self made.

Find the specific heat of the material.

Solution

We can write the specific heat as a function of sensible heat, mass and temperature variation according to the formula:

cp = Q / (m ΔT)

Substituting the data we have the following:

cp = 1150 cal / (360.16 g * (140 ℃ - 37 ℃)) = 0.0310 cal / (g ℃)

But since one calorie equals 4.1813 J, the result can also be expressed as

cp = 0.130 J / (g ℃)

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. Tippens, P. 2011. Physics: Concepts and Applications. 7th. Revised edition. McGraw Hill. 350 - 368.
4. Rex, A. 2011. Fundamentals of Physics. Pearson. 309-332.
5. Sears, Zemansky. 2016. University Physics with Modern Physics. 14 ^th. Volume1. 556-553.
6. Serway, R., Vulle, C. 2011. Fundamentals of Physics. 9 ^na Cengage Learning. 362-374.