Formula for finding heat in physics. Calculation of the amount of heat required to heat a body or released by it during cooling

The internal energy of a thermodynamic system can be changed in two ways:

doing over system work,
using thermal interaction.

The transfer of heat to a body is not associated with the performance of macroscopic work on the body. IN in this case change internal energy caused by the fact that individual molecules of a body with a higher temperature do work on some molecules of a body that has a lower temperature. In this case, thermal interaction is realized due to thermal conductivity. Energy transfer is also possible using radiation. The system of microscopic processes (relating not to the whole body, but to individual molecules) is called heat transfer. The amount of energy that is transferred from one body to another as a result of heat transfer is determined by the amount of heat that is transferred from one body to another.

Definition

Warmth is the energy that is received (or given up) by a body in the process of heat exchange with surrounding bodies (environment).

The symbol for heat is usually the letter Q.

This is one of the basic quantities in thermodynamics. Heat is included in the mathematical expressions of the first and second laws of thermodynamics. Heat is said to be energy in the form of molecular motion.

Heat can be transferred to the system (body), or it can be taken from it. It is believed that if heat is transferred to the system, then it is positive.

Formula for calculating heat when temperature changes Elementary quantity of heat

let's denote it as . Let us note that the element of heat that the system receives (gives) with a small change in its state is not a complete differential. The reason for this is that heat is a function of the process of changing the state of the system.

The elementary amount of heat that is imparted to the system, and the temperature changes from T to T+dT, is equal to:

where C is the heat capacity of the body. If the body in question is homogeneous, then formula (1) for the amount of heat can be represented as: where is the specific heat capacity of the body, m – body mass , - molar heat capacity, – molar mass

If the body is homogeneous, and the heat capacity is considered independent of temperature, then the amount of heat () that the body receives when its temperature increases by an amount can be calculated as:

where t 2, t 1 body temperatures before and after heating. Please note that when finding the difference () in calculations, temperatures can be substituted both in degrees Celsius and in kelvins.

Formula for the amount of heat during phase transitions

The transition from one phase of a substance to another is accompanied by the absorption or release of a certain amount of heat, which is called the heat of phase transition.

So, to transfer an element of matter from a solid state to a liquid, it should be given an amount of heat () equal to:

Where - specific heat melting, dm – element of body mass. It should be taken into account that the body must have a temperature equal to the melting point of the substance in question. During crystallization, heat is released equal to (4).

The amount of heat (heat of evaporation) required to convert liquid into vapor can be found as:

where r is the specific heat of evaporation. When steam condenses, heat is released. The heat of evaporation is equal to the heat of condensation of equal masses of substance.

Units for measuring the amount of heat

The basic unit of measurement for the amount of heat in the SI system is: [Q]=J

An extra-system unit of heat, which is often found in technical calculations. [Q]=cal (calorie). 1 cal=4.1868 J.

Examples of problem solving

Example

Exercise. What volumes of water should be mixed to obtain 200 liters of water at a temperature of t = 40C, if the temperature of one mass of water is t 1 = 10 C, the temperature of the second mass of water is t 2 = 60 C?

Solution. Let us write the heat balance equation in the form:

where Q=cmt is the amount of heat prepared after mixing the water; Q 1 = cm 1 t 1 - the amount of heat of a part of water with temperature t 1 and mass m 1; Q 2 = cm 2 t 2 - the amount of heat of a part of water with temperature t 2 and mass m 2.

From equation (1.1) it follows:

When combining cold (V 1) and hot (V 2) parts of water into a single volume (V), we can assume that:

So, we get a system of equations:

Having solved it we get:

What will heat up faster on the stove - a kettle or a bucket of water? The answer is obvious - a teapot. Then the second question is why?

The answer is no less obvious - because the mass of water in the kettle is less. Great. And now you can do a real physical experience yourself at home. To do this you will need two identical small saucepans, equal amount water and vegetable oil, for example, half a liter and a stove. Place saucepans with oil and water on the same heat. Now just watch what will heat up faster. If you have a thermometer for liquids, you can use it; if not, you can simply test the temperature with your finger from time to time, just be careful not to get burned. In any case, you will soon see that the oil heats up much faster than water. And one more question, which can also be implemented in the form of experience. What will boil faster - warm water or cold? Everything is obvious again - the warm one will be first at the finish line. Why all these strange questions and experiments? To determine the physical quantity called “amount of heat”.

Quantity of heat

The amount of heat is the energy that a body loses or gains during heat transfer. This is clear from the name. When cooling, the body will lose a certain amount of heat, and when heating, it will absorb. And the answers to our questions showed us What does the amount of heat depend on? Firstly, the greater the mass of a body, the greater the amount of heat that must be expended to change its temperature by one degree. Secondly, the amount of heat required to heat a body depends on the substance of which it consists, that is, on the type of substance. And thirdly, the difference in body temperature before and after heat transfer is also important for our calculations. Based on the above, we can determine the amount of heat using the formula:

Q=cm(t_2-t_1) ,

where Q is the amount of heat,
m - body weight,
(t_2-t_1) - the difference between the initial and final body temperatures,
c is the specific heat capacity of the substance, found from the corresponding tables.

Using this formula, you can calculate the amount of heat that is necessary to heat any body or that this body will release when cooling.

The amount of heat is measured in joules (1 J), like any type of energy. However, this value was introduced not so long ago, and people began measuring the amount of heat much earlier. And they used a unit that is widely used in our time - calorie (1 cal). 1 calorie is the amount of heat required to heat 1 gram of water by 1 degree Celsius. Guided by these data, those who like to count calories in the food they eat can, for fun, calculate how many liters of water can be boiled with the energy they consume with food during the day.

As we already know, the internal energy of a body can change both when doing work and through heat transfer (without doing work).

The main difference between work and the amount of heat is that work determines the process of converting the internal energy of the system, which is accompanied by the transformation of energy from one type to another. In the event that a change in internal energy occurs with the help of heat transfer , the transfer of energy from one body to another is carried out due to thermal conductivity , radiation, or.

convection The energy that a body loses or gains during heat transfer is called

amount of heat.

When calculating the amount of heat, you need to know what quantities influence it.

We will heat two vessels using two identical burners. One vessel contains 1 kg of water, the other contains 2 kg. The temperature of the water in the two vessels is initially the same. We can see that during the same time, the water in one of the vessels heats up faster, although both vessels receive an equal amount of heat.

Thus, we conclude: the greater the mass of a given body, the greater the amount of heat that must be expended in order to lower or increase its temperature by the same number of degrees.

When a body cools down, it gives off a greater amount of heat to neighboring objects, the greater its mass.

We all know that if we need to heat a full kettle of water to a temperature of 50°C, we will spend less time on this action than to heat a kettle with the same volume of water, but only to 100°C. In case number one, less heat will be given to the water than in case two. Thus, the amount of heat required for heating directly depends on whether how many degrees the body can warm up. We can conclude:

the amount of heat directly depends on the difference in body temperature.

But is it possible to determine the amount of heat required not to heat water, but some other substance, say, oil, lead or iron?

Fill one vessel with water and fill the other with vegetable oil. The masses of water and oil are equal. We will heat both vessels evenly on identical burners. Let's start the experiment at equal initial temperatures of vegetable oil and water. Five minutes later, having measured the temperatures of the heated oil and water, we will notice that the temperature of the oil is much higher than the temperature of the water, although both liquids received the same amount of heat. When heating equal masses of oil and water at the same temperature, different amounts of heat are required.

And we immediately draw another conclusion: the amount of heat required to heat a body directly depends on the substance of which the body itself consists (the type of substance).

Thus, the amount of heat needed to heat a body (or released when cooling) directly depends on the mass of the body, the variability of its temperature, and the type of substance.

The amount of heat is denoted by the symbol Q. Like others different kinds energy, the amount of heat is measured in joules (J) or kilojoules (kJ).

1 kJ = 1000 J

However, history shows that scientists began to measure the amount of heat long before the concept of energy appeared in physics. At that time, a special unit was developed for measuring the amount of heat - calorie (cal) or kilocalorie (kcal). The word has Latin roots, calor - heat.

1 kcal = 1000 cal

Calorie– this is the amount of heat needed to heat 1 g of water by 1°C

1 cal = 4.19 J ≈ 4.2 J

1 kcal = 4190 J ≈ 4200 J ≈ 4.2 kJ

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What will heat up faster on the stove - a kettle or a bucket of water? The answer is obvious - a teapot. Then the second question is why?

The answer is no less obvious - because the mass of water in the kettle is less. Great. And now you can do a real physical experience yourself at home. To do this, you will need two identical small saucepans, an equal amount of water and vegetable oil, for example, half a liter each and a stove. Place saucepans with oil and water on the same heat. Now just watch what will heat up faster. If you have a thermometer for liquids, you can use it; if not, you can simply test the temperature with your finger from time to time, just be careful not to get burned. In any case, you will soon see that the oil heats up much faster than water. And one more question, which can also be implemented in the form of experience. What will boil faster - warm water or cold? Everything is obvious again - the warm one will be first at the finish line. Why all these strange questions and experiments? To determine the physical quantity called “amount of heat”.

Quantity of heat

Using this formula, you can calculate the amount of heat that is necessary to heat any body or that this body will release when cooling.

The process of transferring energy from one body to another without doing work is called heat exchange or heat transfer. Heat exchange occurs between bodies having different temperatures. When contact is established between bodies with different temperatures, part of the internal energy is transferred from a body with a higher temperature to a body with a lower temperature. The energy transferred to a body as a result of heat exchange is called amount of heat.

Specific heat capacity of a substance:

If the heat transfer process is not accompanied by work, then, based on the first law of thermodynamics, the amount of heat is equal to the change in the internal energy of the body: .

The average energy of the random translational motion of molecules is proportional to the absolute temperature. The change in the internal energy of a body is equal to the algebraic sum of the changes in the energy of all atoms or molecules, the number of which is proportional to the mass of the body, therefore the change in internal energy and, therefore, the amount of heat is proportional to the mass and the change in temperature:

The proportionality factor in this equation is called specific heat capacity of a substance. Specific heat capacity shows how much heat is needed to heat 1 kg of a substance by 1 K.

Work in thermodynamics:

In mechanics, work is defined as the product of the moduli of force and displacement and the cosine of the angle between them. Work is done when a force acts on a moving body and is equal to the change in its kinetic energy.

In thermodynamics, the movement of a body as a whole is not considered; we are talking about the movement of parts of a macroscopic body relative to each other. As a result, the volume of the body changes, but its speed remains equal to zero. Work in thermodynamics is defined in the same way as in mechanics, but is equal to the change not in the kinetic energy of the body, but in its internal energy.

When work is performed (compression or expansion), the internal energy of the gas changes. The reason for this is: during elastic collisions of gas molecules with a moving piston, their kinetic energy changes.

Let us calculate the work done by the gas during expansion. The gas exerts a force on the piston
, Where - gas pressure, and - surface area piston When gas expands, the piston moves in the direction of the force short distance
. If the distance is small, then the gas pressure can be considered constant. The work done by the gas is:

Where
- change in gas volume.

In the process of gas expansion, it does positive work, since the direction of the force and displacement coincide. During the expansion process, the gas releases energy to surrounding bodies.

The work done by external bodies on a gas differs from the work done by a gas only in sign
, since the strength acting on the gas is opposite to the force , with which the gas acts on the piston, and is equal to it in modulus (Newton’s third law); but the movement remains the same. Therefore, the work of external forces is equal to:

First law of thermodynamics:

The first law of thermodynamics is the law of conservation of energy, extended to thermal phenomena. Law of energy conservation: Energy in nature does not arise from nothing and does not disappear: the amount of energy is unchanged, it only passes from one form to another.

Thermodynamics considers bodies whose center of gravity remains virtually unchanged. The mechanical energy of such bodies remains constant, and only the internal energy can change.

Internal energy can change in two ways: heat transfer and work. In the general case, internal energy changes both due to heat transfer and due to work done. The first law of thermodynamics is formulated precisely for such general cases:

The change in the internal energy of a system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system:

If the system is isolated, then no work is done on it and it does not exchange heat with surrounding bodies. According to the first law of thermodynamics the internal energy of an isolated system remains unchanged.

Considering that
, the first law of thermodynamics can be written as follows:

The amount of heat transferred to the system goes to change its internal energy and to perform work on external bodies by the system.

Second law of thermodynamics: It is impossible to transfer heat from a colder system to a hotter one in the absence of other simultaneous changes in both systems or in surrounding bodies.