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
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:
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.
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
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.
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 by it 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 us remind you 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 |
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Quantity of heat |
The internal energy of a thermodynamic system can be changed in two ways:
- doing work on the system,
- using thermal interaction.
The transfer of heat to a body is not associated with the performance of macroscopic work on the body. In this case, the change in internal energy is 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
Let us denote the elementary amount of heat 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 is the mass of the body, is the molar heat capacity, is the molar mass of the substance, is the number of moles of the substance.
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 temperature 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
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 is the specific heat of fusion, dm is the 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:
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.
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.
The obvious conclusion is: 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 quantity of heat is denoted by the symbol Q. Like other different types of energy, the quantity 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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