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: a body of greater mass gives off more heat when cooled. 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 by a physical quantity called specific heat capacity of a substance.
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. Subtract the smaller temperature from the larger 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 form;
- 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 is heated from temperature \(t_2 \) to temperature \(t \) .
4. Solution of the problem in general form. The amount of heat given off by 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 the amount of heat \(Q \) to a solid body with mass \(m \) , the 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
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 the internal energy of a body during heat transfer is characterized by a quantity called the amount of heat.
is a change in the internal energy of a body during the process of heat transfer without performing work. The amount of heat is indicated by the letter Q .
Work, internal energy and heat are measured in the same units - joules ( J), like any type of energy.
In thermal measurements, a special unit of energy was previously used as a unit of heat quantity - the calorie ( feces), equal to the amount of heat required to heat 1 gram of water by 1 degree Celsius (more precisely, from 19.5 to 20.5 ° C). This unit, in particular, is currently used when calculating heat consumption (thermal energy) in apartment buildings. The mechanical equivalent of heat has been experimentally established - the relationship between calorie and joule: 1 cal = 4.2 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.
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 body mass, the greater the amount of heat it requires to warm up. It's the same with cooling.
The amount of heat required to heat a body also depends on the type of substance from which the body is made. This dependence of the amount of heat required to heat a body on the type of substance is characterized by a physical quantity called specific heat capacity substances.
is 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). 1 kg of substance releases the same amount of heat when cooled by 1 °C.
Specific heat capacity is designated by the letter With. 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.
Since the amount of heat is equal to the change in the internal energy of the body, we can say that the specific heat capacity shows how much the internal energy changes 1 kg substance 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.
Q required to heat a body of mass m on temperature t 1 °С up to temperature t 2 °С, 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 = c ∙ m (t 2 - t 1)
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. Subtract the smaller temperature from the larger temperature.
This is a summary of the topic "Quantity of heat. Specific heat". Select next steps:
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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).
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Given: |
SI |
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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.
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Required quantity |
Designation |
Units |
Basic formula |
Formula for quantity |
|
Quantity of heat |
(or heat transfer).
Specific heat capacity of a substance.
Heat capacity- this is the amount of heat absorbed by a body when heated by 1 degree.
The heat capacity of a body is indicated by a capital Latin letter WITH.
What does the heat capacity of a body depend on? First of all, from its mass. It is clear that heating, for example, 1 kilogram of water will require more heat than heating 200 grams.
What about the type of substance? Let's do an experiment. Let's take two identical vessels and, having poured water weighing 400 g into one of them, and vegetable oil weighing 400 g into the other, we will begin to heat them using identical burners. By observing the thermometer readings, we will see that the oil heats up quickly. To heat water and oil to the same temperature, the water must be heated longer. But the longer we heat the water, the more heat it receives from the burner.
Thus, heating the same mass of different substances to the same temperature requires different amounts of heat. The amount of heat required to heat a body and, therefore, its heat capacity depend on the type of substance of which the body is composed.
So, for example, to increase the temperature of water weighing 1 kg by 1°C, an amount of heat equal to 4200 J is required, and to heat the same mass of sunflower oil by 1°C, an amount of heat equal to 1700 J is required.
A physical quantity showing how much heat is required to heat 1 kg of a substance by 1 ºС is called specific heat capacity of this substance.
Each substance has its own specific heat capacity, which is denoted by the Latin letter c and measured in joules per kilogram degree (J/(kg °C)).
The specific heat capacity of the same substance in different states of aggregation (solid, liquid and gaseous) is different. For example, the specific heat capacity of water is 4200 J/(kg °C), and the specific heat capacity of ice is 2100 J/(kg °C); aluminum in the solid state has a specific heat capacity of 920 J/(kg - °C), and in the liquid state - 1080 J/(kg - °C).
Note that water has a very high specific heat capacity. Therefore, water in the seas and oceans, heating up in summer, absorbs a large amount of heat from the air. Thanks to this, in those places that are located near large bodies of water, summer is not as hot as in places far from the water.
Calculation of the amount of heat required to heat a body or released by it during cooling.
From the above it is clear that the amount of heat required to heat a body depends on the type of substance of which the body consists (i.e., its specific heat capacity) and on the mass of the body. It is also clear that the amount of heat depends on how many degrees we are going to increase the body temperature.
So, to determine the amount of heat required to heat a body or released by it during cooling, you need to multiply the specific heat capacity of the body by its mass and by the difference between its final and initial temperatures:
Q = cm (t 2 - t 1 ) ,
Where Q- quantity of heat, c— specific heat capacity, m- body mass , t 1 — initial temperature, t 2 — final temperature.
When the body heats up t 2 > t 1 and therefore Q > 0 . When the body cools down t 2i< t 1 and therefore Q< 0 .
If the heat capacity of the entire body is known WITH, Q determined by the formula:
Q = C (t 2 - t 1 ) .
The internal energy of a body can change due to the work of external forces. To characterize the change in internal energy during heat transfer, a quantity called the amount of heat and denoted Q is introduced.
In the international system, the unit of heat, as well as work and energy, is the joule: = = = 1 J.
In practice, a non-systemic unit of heat quantity is sometimes used - the calorie. 1 cal. = 4.2 J.
It should be noted that the term “quantity of heat” is unfortunate. It was introduced at a time when it was believed that bodies contained some weightless, elusive liquid - caloric. The process of heat exchange supposedly consists in the fact that caloric, flowing from one body to another, carries with it a certain amount of heat. Now, knowing the basics of the molecular-kinetic theory of the structure of matter, we understand that there is no caloric in bodies, the mechanism for changing the internal energy of a body is different. However, the power of tradition is great and we continue to use a term introduced on the basis of incorrect ideas about the nature of heat. At the same time, understanding the nature of heat transfer, one should not completely ignore misconceptions about it. On the contrary, by drawing an analogy between the flow of heat and the flow of a hypothetical liquid of caloric, the amount of heat and the amount of caloric, when solving certain classes of problems, it is possible to visualize the ongoing processes and correctly solve the problems. In the end, the correct equations describing heat transfer processes were once obtained on the basis of incorrect ideas about caloric as a heat carrier.
Let us consider in more detail the processes that can occur as a result of heat exchange.
Pour some water into the test tube and close it with a stopper. We hang the test tube from a rod fixed in a stand and place an open flame under it. The test tube receives a certain amount of heat from the flame and the temperature of the liquid in it rises. As the temperature increases, the internal energy of the liquid increases. An intensive process of vaporization occurs. Expanding liquid vapors perform mechanical work to push the stopper out of the test tube.
Let's conduct another experiment with a model of a cannon made from a piece of brass tube, which is mounted on a cart. On one side the tube is tightly closed with an ebonite plug through which a pin is passed. Wires are soldered to the pin and tube, ending in terminals to which voltage can be supplied from the lighting network. The cannon model is thus a type of electric boiler.
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Pour some water into the cannon barrel and close the tube with a rubber stopper. Let's connect the gun to a power source. Electric current passing through water heats it. The water boils, which leads to intense steam formation. The pressure of water vapor increases and, finally, they do the work of pushing the plug out of the gun barrel.
The gun, due to recoil, rolls away in the direction opposite to the ejection of the plug.
Both experiences are united by the following circumstances. In the process of heating the liquid in various ways, the temperature of the liquid and, accordingly, its internal energy increased. In order for the liquid to boil and evaporate intensively, it was necessary to continue heating it.
Liquid vapors, due to their internal energy, performed mechanical work.
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We investigate the dependence of the amount of heat required to heat a body on its mass, temperature changes and the type of substance. To study these dependencies we will use water and oil. (To measure temperature in the experiment, an electric thermometer made of a thermocouple connected to a mirror galvanometer is used. One thermocouple junction is lowered into a vessel with cold water to ensure its constant temperature. The other thermocouple junction measures the temperature of the liquid under study).
The experience consists of three series. In the first series, for a constant mass of a specific liquid (in our case, water), the dependence of the amount of heat required to heat it on temperature changes is studied. We will judge the amount of heat received by the liquid from the heater (electric stove) by the heating time, assuming that there is a directly proportional relationship between them. For the result of the experiment to correspond to this assumption, it is necessary to ensure a stationary heat flow from the electric stove to the heated body. To do this, the electric stove was turned on in advance, so that by the beginning of the experiment, the temperature of its surface would cease to change. To heat the liquid more evenly during the experiment, we will stir it using the thermocouple itself. We will record the thermometer readings at regular intervals until the light spot reaches the edge of the scale.
Let us conclude: there is a direct proportional relationship between the amount of heat required to heat a body and the change in its temperature.
In the second series of experiments we will compare the amounts of heat required to heat identical liquids of different masses when their temperature changes by the same amount.
For the convenience of comparing the obtained values, the mass of water for the second experiment will be taken to be two times less than in the first experiment.
We will again record the thermometer readings at regular intervals.
Comparing the results of the first and second experiments, the following conclusions can be drawn.
In the third series of experiments we will compare the amounts of heat required to heat equal masses of different liquids when their temperature changes by the same amount.
We will heat oil on an electric stove, the mass of which is equal to the mass of water in the first experiment. We will record the thermometer readings at regular intervals.
The result of the experiment confirms the conclusion that the amount of heat required to heat a body is directly proportional to the change in its temperature and, in addition, indicates the dependence of this amount of heat on the type of substance.
Since the experiment used oil, the density of which is less than the density of water, and heating the oil to a certain temperature required less heat than heating water, it can be assumed that the amount of heat required to heat a body depends on its density.
To test this assumption, we will simultaneously heat equal masses of water, paraffin and copper on a constant power heater.
After the same time, the temperature of copper is approximately 10 times, and paraffin approximately 2 times higher than the temperature of water.
But copper has a higher density and paraffin has a lower density than water.
Experience shows that the quantity characterizing the rate of change in temperature of the substances from which the bodies involved in heat exchange are made is not density. This quantity is called the specific heat capacity of a substance and is denoted by the letter c.
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A special device is used to compare the specific heat capacities of different substances. The device consists of racks in which a thin paraffin plate and a strip with rods passed through it are attached. Aluminum, steel and brass cylinders of equal mass are fixed at the ends of the rods.
Let's heat the cylinders to the same temperature by immersing them in a vessel with water standing on a hot stove. We secure the hot cylinders to the racks and release them from the fastening. The cylinders simultaneously touch the paraffin plate and, melting the paraffin, begin to sink into it. The depth of immersion of cylinders of the same mass into a paraffin plate, when their temperature changes by the same amount, turns out to be different.
Experience shows that the specific heat capacities of aluminum, steel and brass are different.
Having carried out appropriate experiments with the melting of solids, vaporization of liquids, and combustion of fuel, we obtain the following quantitative dependencies.
To obtain units of specific quantities, they must be expressed from the corresponding formulas and into the resulting expressions substitute units of heat - 1 J, mass - 1 kg, and for specific heat capacity - 1 K.
We get the following units: specific heat capacity – 1 J/kg·K, other specific heats: 1 J/kg.