The internal energy of a body changes when work is performed or heat is transferred. In the phenomenon of heat transfer, internal energy is transferred by conduction, convection or radiation.
Each body, when heated or cooled (through heat transfer), gains or loses some amount of energy. Based on this, it is customary to call this amount of energy the amount of heat.
So, the amount of heat is the energy that a body gives or receives during the process of heat transfer.
How much heat is needed to heat water? On simple example you can understand that heating different amounts of water will require different quantities warmth. Let's say we take two test tubes with 1 liter of water and 2 liters of water. In which case will more heat be required? In the second, where there are 2 liters of water in a test tube. The second test tube will take longer to heat up if we heat them with the same fire source.
Thus, the amount of heat depends on body mass. The greater the mass, the greater the amount of heat required for heating and, accordingly, the longer it takes to cool the body.
What else does the amount of heat depend on? Naturally, from the difference in body temperatures. But that is not all. After all, if we try to heat water or milk, we will need different amounts of time. That is, it turns out that the amount of heat depends on the substance of which the body consists.
As a result, it turns out that the amount of heat that is needed for heating or the amount of heat that is released when a body cools depends on its mass, on the change in temperature and on the type of substance of which the body is composed.
How is the amount of heat measured?
Behind unit of heat it is generally accepted 1 Joule. Before the advent of the unit of measurement of energy, scientists considered the amount of heat as calories. This unit of measurement is usually abbreviated as “J”
Calorie- this is the amount of heat that is necessary to heat 1 gram of water by 1 degree Celsius. The abbreviated form of calorie measurement is “cal”.
1 cal = 4.19 J.
Please note that in these energy units it is customary to note nutritional value food products kJ and kcal.
1 kcal = 1000 cal.
1 kJ = 1000 J
1 kcal = 4190 J = 4.19 kJ
What is specific heat capacity
Each substance in nature has its own properties, and heating each individual substance requires a different amount of energy, i.e. amount of heat.
Specific heat capacity of a substance- this is a quantity equal to the amount of heat that needs to be transferred to a body with a mass of 1 kilogram in order to heat it to a temperature of 1 0 C
Specific heat capacity is designated by the letter c and has a measurement value of J/kg*
For example, the specific heat capacity of water is 4200 J/kg* 0 C. That is, this is the amount of heat that needs to be transferred to 1 kg of water to heat it by 1 0 C
It should be remembered that the specific heat capacity of substances in different states of aggregation is different. That is, to heat the ice by 1 0 C will require a different amount of heat.
How to calculate the amount of heat to heat a body
For example, it is necessary to calculate the amount of heat that needs to be spent in order to heat 3 kg of water from a temperature of 15 0 C up to temperature 85 0 C. We know the specific heat capacity of water, that is, the amount of energy that is needed to heat 1 kg of water by 1 degree. That is, in order to find out the amount of heat in our case, you need to multiply the specific heat capacity of water by 3 and by the number of degrees by which you want to increase the water temperature. So that's 4200*3*(85-15) = 882,000.
In brackets we calculate the exact number of degrees, subtracting from the final required result initial
So, in order to heat 3 kg of water from 15 to 85 0 C, we need 882,000 J of heat.
The amount of heat is denoted by the letter Q, the formula for calculating it is as follows:
Q=c*m*(t 2 -t 1).
Analysis and solution of problems
Problem 1. How much heat is required to heat 0.5 kg of water from 20 to 50 0 C
Given:
m = 0.5 kg.,
s = 4200 J/kg* 0 C,
t 1 = 20 0 C,
t 2 = 50 0 C.
We determined the specific heat capacity from the table.
Solution:
2 -t 1 ).
Substitute the values:
Q=4200*0.5*(50-20) = 63,000 J = 63 kJ.
Answer: Q=63 kJ.
Task 2. What amount of heat is required to heat an aluminum bar weighing 0.5 kg by 85 0 C?
Given:
m = 0.5 kg.,
s = 920 J/kg* 0 C,
t 1 = 0 0 C,
t 2 = 85 0 C.
Solution:
the amount of heat is determined by the formula Q=c*m*(t 2 -t 1 ).
Substitute the values:
Q=920*0.5*(85-0) = 39,100 J = 39.1 kJ.
Answer: Q= 39.1 kJ.
1. The change in internal energy by doing work is characterized by the amount of work, i.e. work is a measure of the change in internal energy in a given process. The change in internal energy of a body during heat transfer is characterized by a quantity called amount of heat.
The amount of heat is the change in the internal energy of a body during the process of heat transfer without doing work.
The amount of heat is denoted by the letter \(Q\) . Since the amount of heat is a measure of the change in internal energy, its unit is the joule (1 J).
When a body transfers a certain amount of heat without doing work, its internal energy increases; if the body gives off a certain amount of heat, then its internal energy decreases.
2. If you pour 100 g of water into two identical vessels, one and 400 g into the other at the same temperature and place them on identical burners, then the water in the first vessel will boil earlier. Thus, the greater the mass of a body, the greater the amount of heat it requires to heat up. The same is true with cooling: when a body of greater mass is cooled, it gives off a greater amount of heat. These bodies are made of the same substance and they heat up or cool down by the same number of degrees.
3. If we now heat 100 g of water from 30 to 60 °C, i.e. at 30 °C, and then up to 100 °C, i.e. by 70 °C, then in the first case it will take less time to heat up than in the second, and, accordingly, heating water by 30 °C will require less heat than heating water by 70 °C. Thus, the amount of heat is directly proportional to the difference between the final \((t_2\,^\circ C) \) and initial \((t_1\,^\circ C) \) temperatures: \(Q\sim(t_2- t_1) \) .
4. If you now pour 100 g of water into one vessel, and pour a little water into another identical vessel and put in it a metal body such that its mass and the mass of water are 100 g, and heat the vessels on identical tiles, then you will notice that in a vessel containing only water will have a lower temperature than one containing water and a metal body. Therefore, in order for the temperature of the contents in both vessels to be the same, it is necessary to transfer more heat to the water than to the water and the metal body. Thus, the amount of heat required to heat a body depends on the type of substance from which the body is made.
5. The dependence of the amount of heat required to heat a body on the type of substance is characterized physical quantity, called specific heat capacity substances.
A physical quantity equal to the amount of heat that must be imparted to 1 kg of a substance to heat it by 1 ° C (or 1 K) is called the specific heat capacity of the substance.
1 kg of substance releases the same amount of heat when cooled by 1 °C.
Specific heat capacity is denoted by the letter \(c\) . The unit of specific heat capacity is 1 J/kg °C or 1 J/kg K.
The specific heat capacity of substances is determined experimentally. Liquids have a higher specific heat capacity than metals; Water has the highest specific heat, gold has a very small specific heat.
The specific heat of lead is 140 J/kg °C. This means that to heat 1 kg of lead by 1 °C it is necessary to expend an amount of heat of 140 J. The same amount of heat will be released when 1 kg of water cools by 1 °C.
Since the amount of heat is equal to the change in the internal energy of the body, we can say that specific heat capacity shows how much the internal energy of 1 kg of a substance changes when its temperature changes by 1 °C. In particular, the internal energy of 1 kg of lead increases by 140 J when heated by 1 °C, and decreases by 140 J when cooled.
The amount of heat \(Q \) required to heat a body of mass \(m \) from temperature \((t_1\,^\circ C) \) to temperature \((t_2\,^\circ C) \) is equal to the product of the specific heat capacity of the substance, body mass and the difference between the final and initial temperatures, i.e.
\[ Q=cm(t_2()^\circ-t_1()^\circ) \]
The same formula is used to calculate the amount of heat that a body gives off when cooling. Only in this case should the final temperature be subtracted from the initial temperature, i.e. from greater value subtract the lesser temperature.
6. Example of problem solution. 100 g of water at a temperature of 20 °C is poured into a glass containing 200 g of water at a temperature of 80 °C. After which the temperature in the vessel reached 60 °C. How much heat did the cold water receive and how much heat did the hot water give out?
When solving a problem, you must perform the following sequence of actions:
- write down briefly the conditions of the problem;
- convert the values of quantities to SI;
- analyze the problem, establish which bodies are involved in heat exchange, which bodies give off energy and which receive;
- solve the problem in general view;
- perform calculations;
- analyze the received answer.
1. The task.
Given:
\(m_1 \) = 200 g
\(m_2\) = 100 g
\(t_1 \) = 80 °C
\(t_2 \) = 20 °C
\(t\) = 60 °C
______________
\(Q_1 \) — ? \(Q_2 \) — ?
\(c_1 \) = 4200 J/kg °C
2. SI:\(m_1\) = 0.2 kg; \(m_2\) = 0.1 kg.
3. Task Analysis. The problem describes the process of heat exchange between hot and cold water. Hot water gives off an amount of heat \(Q_1 \) and cools from temperature \(t_1 \) to temperature \(t \) . Cold water receives the amount of heat \(Q_2 \) and heats up from temperature \(t_2 \) to temperature \(t \) .
4. Solution of the problem in general form. The amount of heat given hot water, is calculated by the formula: \(Q_1=c_1m_1(t_1-t) \) .
The amount of heat received by cold water is calculated by the formula: \(Q_2=c_2m_2(t-t_2) \) .
5.
Computations.
\(Q_1 \) = 4200 J/kg · °С · 0.2 kg · 20 °С = 16800 J
\(Q_2\) = 4200 J/kg °C 0.1 kg 40 °C = 16800 J
6. The answer is that the amount of heat given off by hot water is equal to the amount of heat received by cold water. In this case, an idealized situation was considered and it was not taken into account that a certain amount of heat was used to heat the glass in which the water was located and the surrounding air. In reality, the amount of heat given off by hot water is greater than the amount of heat received by cold water.
Part 1
1. The specific heat capacity of silver is 250 J/(kg °C). What does this mean?
1) when 1 kg of silver cools at 250 °C, an amount of heat of 1 J is released
2) when 250 kg of silver cools by 1 °C, an amount of heat of 1 J is released
3) when 250 kg of silver cools by 1 °C, an amount of heat of 1 J is absorbed
4) when 1 kg of silver cools by 1 °C, an amount of heat of 250 J is released
2. The specific heat capacity of zinc is 400 J/(kg °C). It means that
1) when 1 kg of zinc is heated by 400 °C, its internal energy increases by 1 J
2) when 400 kg of zinc is heated by 1 °C, its internal energy increases by 1 J
3) to heat 400 kg of zinc by 1 °C it is necessary to expend 1 J of energy
4) when 1 kg of zinc is heated by 1 °C, its internal energy increases by 400 J
3. When transferring solid body mass \(m \) amount of heat \(Q \) body temperature increased by \(\Delta t^\circ \) . Which of the following expressions determines the specific heat capacity of the substance of this body?
1) \(\frac(m\Delta t^\circ)(Q) \)
2) \(\frac(Q)(m\Delta t^\circ) \)
3) \(\frac(Q)(\Delta t^\circ) \)
4) \(Qm\Delta t^\circ \)
4. The figure shows a graph of the dependence of the amount of heat required to heat two bodies (1 and 2) of the same mass on temperature. Compare the specific heat capacity values (\(c_1 \) and \(c_2 \) ) of the substances from which these bodies are made.
1) \(c_1=c_2 \)
2) \(c_1>c_2 \)
3)\(c_1
5. The diagram shows the amount of heat transferred to two bodies of equal mass when their temperature changes by the same number of degrees. Which relationship is correct for the specific heat capacities of the substances from which bodies are made?
1) \(c_1=c_2\)
2) \(c_1=3c_2\)
3) \(c_2=3c_1\)
4) \(c_2=2c_1\)
6. The figure shows a graph of the temperature of a solid body depending on the amount of heat it gives off. Body weight 4 kg. What is the specific heat capacity of the substance of this body?
1) 500 J/(kg °C)
2) 250 J/(kg °C)
3) 125 J/(kg °C)
4) 100 J/(kg °C)
7. When heating a crystalline substance weighing 100 g, the temperature of the substance and the amount of heat imparted to the substance were measured. The measurement data was presented in table form. Assuming that energy losses can be neglected, determine the specific heat capacity of the substance in the solid state.
1) 192 J/(kg °C)
2) 240 J/(kg °C)
3) 576 J/(kg °C)
4) 480 J/(kg °C)
8. To heat 192 g of molybdenum by 1 K, you need to transfer an amount of heat of 48 J to it. What is the specific heat of this substance?
1) 250 J/(kg K)
2) 24 J/(kg K)
3) 4·10 -3 J/(kg K)
4) 0.92 J/(kg K)
9. What amount of heat is needed to heat 100 g of lead from 27 to 47 °C?
1) 390 J
2) 26 kJ
3) 260 J
4) 390 kJ
10. Heating a brick from 20 to 85 °C requires the same amount of heat as heating water of the same mass by 13 °C. The specific heat capacity of the brick is
1) 840 J/(kg K)
2) 21000 J/(kg K)
3) 2100 J/(kg K)
4) 1680 J/(kg K)
11. From the list of statements below, select two correct ones and write their numbers in the table.
1) The amount of heat that a body receives when its temperature increases by a certain number of degrees is equal to the amount of heat that this body gives off when its temperature decreases by the same number of degrees.
2) When a substance cools, its internal energy increases.
3) The amount of heat that a substance receives when heated is used mainly to increase the kinetic energy of its molecules.
4) The amount of heat that a substance receives when heated is used mainly to increase the potential energy of interaction of its molecules
5) The internal energy of a body can be changed only by imparting a certain amount of heat to it
12. The table presents the results of measurements of mass \(m\) , temperature changes \(\Delta t\) and the amount of heat \(Q\) released during cooling of cylinders made of copper or aluminum.
Which statements correspond to the results of the experiment? Select two correct ones from the list provided. Indicate their numbers. Based on the measurements taken, it can be argued that the amount of heat released during cooling
1) depends on the substance from which the cylinder is made.
2) does not depend on the substance from which the cylinder is made.
3) increases with increasing cylinder mass.
4) increases with increasing temperature difference.
5) the specific heat capacity of aluminum is 4 times greater than the specific heat capacity of tin.
Part 2
C1. A solid body weighing 2 kg is placed in a 2 kW furnace and begins to heat up. The figure shows the dependence of the temperature \(t\) of this body on the heating time \(\tau \) . What is the specific heat capacity of the substance?
1) 400 J/(kg °C)
2) 200 J/(kg °C)
3) 40 J/(kg °C)
4) 20 J/(kg °C)
Answers
In this lesson we will learn how to calculate the amount of heat required to heat a body or released by it when cooling. To do this, we will summarize the knowledge that was acquired in previous lessons.
In addition, we will learn, using the formula for the amount of heat, to express the remaining quantities from this formula and calculate them, knowing other quantities. An example of a problem with a solution for calculating the amount of heat will also be considered.
This lesson is devoted to calculating the amount of heat when a body is heated or released when cooled.
The ability to calculate the required amount of heat is very important. This may be needed, for example, when calculating the amount of heat that needs to be imparted to water to heat a room.
Rice. 1. The amount of heat that must be imparted to the water to heat the room
Or to calculate the amount of heat that is released when fuel is burned in various engines:
Rice. 2. The amount of heat that is released when fuel is burned in the engine
This knowledge is also needed, for example, to determine the amount of heat that is released by the Sun and falls on the Earth:
Rice. 3. The amount of heat released by the Sun and falling on the Earth
To calculate the amount of heat, you need to know three things (Fig. 4):
- body weight (which can usually be measured using a scale);
- the temperature difference by which a body must be heated or cooled (usually measured using a thermometer);
- specific heat capacity of the body (which can be determined from the table).
Rice. 4. What you need to know to determine
The formula by which the amount of heat is calculated looks like this:
The following quantities appear in this formula:
The amount of heat measured in joules (J);
The specific heat capacity of a substance is measured in ;
- temperature difference, measured in degrees Celsius ().
Let's consider the problem of calculating the amount of heat.
Task
A copper glass with a mass of grams contains water with a volume of liter at a temperature. How much heat must be transferred to a glass of water so that its temperature becomes equal to ?
Rice. 5. Illustration of the problem conditions
First we write down a short condition ( Given) and convert all quantities to the international system (SI).
|
Given: |
SI |
|
|
Find: |
Solution:
First, determine what other quantities we need to solve this problem. Using the table of specific heat capacity (Table 1) we find (specific heat capacity of copper, since by condition the glass is copper), (specific heat capacity of water, since by condition there is water in the glass). In addition, we know that to calculate the amount of heat we need a mass of water. According to the condition, we are given only the volume. Therefore, from the table we take the density of water: (Table 2).
Table 1. Specific heat capacity of some substances,
Table 2. Densities of some liquids
Now we have everything we need to solve this problem.
Note that the final amount of heat will consist of the sum of the amount of heat required to heat the copper glass and the amount of heat required to heat the water in it:
Let's first calculate the amount of heat required to heat a copper glass:
Before calculating the amount of heat required to heat water, let’s calculate the mass of water using a formula that is familiar to us from grade 7:
Now we can calculate:
Then we can calculate:
Let's remember what kilojoules mean. The prefix "kilo" means 
.
Answer:.
For the convenience of solving problems of finding the amount of heat (the so-called direct problems) and quantities associated with this concept, you can use the following table.
|
Required quantity |
Designation |
Units |
Basic formula |
Formula for quantity |
|
Quantity of heat |
HEAT EXCHANGE.
1. Heat exchange.
Heat exchange or heat transfer is the process of transferring the internal energy of one body to another without doing work.
There are three types of heat transfer.
1) Thermal conductivity- This is heat exchange between bodies during their direct contact.
2) Convection- This is heat exchange in which heat is transferred by gas or liquid flows.
3) Radiation– This is heat exchange through electromagnetic radiation.
2. Amount of heat.
The amount of heat is a measure of the change in the internal energy of a body during heat exchange. Denoted by the letter Q.
Unit for measuring the amount of heat = 1 J.
The amount of heat received by a body from another body as a result of heat exchange can be spent on increasing temperature (increasing the kinetic energy of molecules) or changing the state of aggregation (increasing potential energy).
3.Specific heat capacity of the substance.
Experience shows that the amount of heat required to heat a body of mass m from temperature T 1 to temperature T 2 is proportional to the mass of the body m and the temperature difference (T 2 - T 1), i.e.
Q = cm(T 2 - T 1 ) = smΔ T,
With is called the specific heat capacity of the substance of the heated body.
The specific heat capacity of a substance is equal to the amount of heat that must be imparted to 1 kg of the substance to heat it by 1 K.
Unit of measurement of specific heat capacity =.
The heat capacity values for various substances can be found in physical tables.
Exactly the same amount of heat Q will be released when the body is cooled by ΔT.
4.Specific heat of vaporization.
Experience shows that the amount of heat required to convert a liquid into steam is proportional to the mass of the liquid, i.e.
Q = Lm,
where is the proportionality coefficient L is called the specific heat of vaporization.
The specific heat of vaporization is equal to the amount of heat required to convert 1 kg of liquid at boiling point into steam.
A unit of measurement for the specific heat of vaporization.
During the reverse process, steam condensation, heat is released in the same amount that was spent on steam formation.
5.Specific heat of fusion.
Experience shows that the amount of heat required to transform a solid into a liquid is proportional to the mass of the body, i.e.
Q = λ m,
where the proportionality coefficient λ is called the specific heat of fusion.
The specific heat of fusion is equal to the amount of heat that is necessary to transform a solid body weighing 1 kg into a liquid at the melting point.
A unit of measurement for the specific heat of fusion.
During the reverse process, crystallization of the liquid, heat is released in the same amount that was spent on melting.
6. Specific heat of combustion.
Experience shows that the amount of heat released during complete combustion of fuel is proportional to the mass of the fuel, i.e.
Q = qm,
Where the proportionality coefficient q is called the specific heat of combustion.
The specific heat of combustion is equal to the amount of heat released during complete combustion of 1 kg of fuel.
Unit of measurement of specific heat of combustion.
7. Heat balance equation.
Heat exchange involves two or more bodies. Some bodies give off heat, while others receive it. Heat exchange occurs until the temperatures of the bodies become equal. According to the law of conservation of energy, the amount of heat that is given out is equal to the amount that is received. On this basis, the heat balance equation is written.
Let's look at an example.
A body of mass m 1, the heat capacity of which is c 1, has a temperature T 1, and a body of mass m 2, the heat capacity of which is c 2, has a temperature T 2. Moreover, T 1 is greater than T 2. These bodies are brought into contact. Experience shows that a cold body (m 2) begins to heat up, and a hot body (m 1) begins to cool. This suggests that part of the internal energy of the hot body is transferred to the cold one, and the temperatures are equalized. Let us denote the final overall temperature by θ. 
The amount of heat transferred from a hot body to a cold one
Q transferred. = c 1 m 1 (T 1 – θ )
The amount of heat received by a cold body from a hot one
Q received. = c 2 m 2 (θ – T 2 )
According to the law of conservation of energy Q transferred. = Q received., i.e.
c 1 m 1 (T 1 – θ )= c 2 m 2 (θ – T 2 )
Let's open the brackets and express the value of the total steady-state temperature θ.
In this case, we obtain the temperature value θ in kelvins.
However, since Q is passed in the expressions. and Q is received. is the difference between two temperatures, and it is the same both in Kelvin and in degrees Celsius, then the calculation can be carried out in degrees Celsius. Then
In this case, we obtain the temperature value θ in degrees Celsius.
The equalization of temperatures as a result of thermal conductivity can be explained on the basis of molecular kinetic theory as the exchange of kinetic energy between molecules upon collision in the process of thermal chaotic motion.
This example can be illustrated with a graph. 
Along with mechanical energy, any body (or system) has internal energy. Internal energy is the energy of rest. It consists of the thermal chaotic movement of the molecules that make up the body, the potential energy of their mutual arrangement, the kinetic and potential energy of electrons in atoms, nucleons in nuclei, and so on.
In thermodynamics, it is important to know not the absolute value of internal energy, but its change.
In thermodynamic processes, only the kinetic energy of moving molecules changes (thermal energy is not enough to change the structure of an atom, much less a nucleus). Therefore, in fact under internal energy in thermodynamics we mean energy thermal chaotic molecular movements.
Internal energy U one mole of an ideal gas is equal to:
Thus, internal energy depends only on temperature. The internal energy U is a function of the state of the system, regardless of background.
It is clear that in the general case, a thermodynamic system can have both internal and mechanical energy, and different systems can exchange these types of energy.
Exchange mechanical energy characterized by perfect work A, and the exchange of internal energy – the amount of heat transferred Q.
For example, in winter you threw a hot stone into the snow. Due to the reserve of potential energy, mechanical work was done to compress the snow, and due to the reserve of internal energy, the snow was melted. If the stone was cold, i.e. If the temperature of the stone is equal to the temperature of the medium, then only work will be done, but there will be no exchange of internal energy.
So, work and heat are not special forms of energy. We cannot talk about the reserve of heat or work. This measure of transferred another system of mechanical or internal energy. We can talk about the reserve of these energies. In addition, mechanical energy can be converted into thermal energy and vice versa. For example, if you hit an anvil with a hammer, then after a while the hammer and the anvil will heat up (this is an example dissipation energy).
We can give many more examples of the transformation of one form of energy into another.
Experience shows that in all cases, The transformation of mechanical energy into thermal energy and vice versa always occurs in strictly equivalent quantities. This is the essence of the first law of thermodynamics, which follows from the law of conservation of energy.
The amount of heat imparted to the body goes to increase internal energy and to perform work on the body:
| , | (4.1.1) |
- That's what it is first law of thermodynamics , or law of conservation of energy in thermodynamics.
Sign rule: if heat is transferred from the environment this system, and if the system performs work on surrounding bodies, in this case . Taking into account the sign rule, the first law of thermodynamics can be written as:
In this expression U– system state function; d U is its total differential, and δ Q and δ A they are not. In each state, the system has a certain and only this value of internal energy, so we can write:
 ,
|
It is important to note that heat Q and work A depend on how the transition from state 1 to state 2 is accomplished (isochorically, adiabatically, etc.), and the internal energy U does not depend. At the same time, it cannot be said that the system has a specific value of heat and work for a given state.
From formula (4.1.2) it follows that the amount of heat is expressed in the same units as work and energy, i.e. in joules (J).
Of particular importance in thermodynamics are circular or cyclic processes in which a system, after passing through a series of states, returns to its original state. Figure 4.1 shows the cyclic process 1– A–2–b–1, while work A was done.
Rice. 4.1
Because U is a state function, then
| (4.1.3) |
This is true for any state function.
If then according to the first law of thermodynamics, i.e. It is impossible to build a periodically operating engine that would perform more work than the amount of energy imparted to it from the outside. In other words, a perpetual motion machine of the first kind is impossible. This is one of the formulations of the first law of thermodynamics.
It should be noted that the first law of thermodynamics does not indicate in which direction the processes of state change occur, which is one of its shortcomings.
