>>Physics: Calculation of the amount of heat required to heat the body and released by it during cooling
To learn how to calculate the amount of heat that is necessary to heat the body, we first establish on what quantities it depends.
From the previous paragraph, we already know that this amount of heat depends on the kind of substance that the body consists of (i.e., its specific heat capacity):
Q depends on c
But that is not all.
If we want to heat the water in the kettle so that it becomes only warm, then we will not heat it for long. And in order for the water to become hot, we will heat it longer. But the longer the kettle is in contact with the heater, the more heat it will receive from it.
Therefore, the more the temperature of the body changes during heating, the more heat must be transferred to it.
Let the initial temperature of the body be equal to tini, and the final temperature - tfin. Then the change in body temperature will be expressed by the difference:
Finally, everyone knows that for heating, for example, 2 kg of water takes more time (and therefore more heat) than it takes to heat 1 kg of water. This means that the amount of heat required to heat up a body depends on the mass of that body:
So, to calculate the amount of heat, you need to know the specific heat capacity of the substance from which the body is made, the mass of this body and the difference between its final and initial temperatures.
Let, for example, it is required to determine how much heat is needed to heat an iron part with a mass of 5 kg, provided that its initial temperature is 20 °C, and the final temperature should be 620 °C.
From table 8 we find that the specific heat capacity of iron is c = 460 J/(kg°C). This means that it takes 460 J to heat 1 kg of iron by 1 °C.
To heat 5 kg of iron by 1 °C, 5 times the amount of heat is required, i.e. 460 J * 5 = 2300 J.
To heat iron not by 1 °C, but by A t \u003d 600 ° C, another 600 times more heat will be required, i.e. 2300 J X 600 \u003d 1 380 000 J. Exactly the same (modulo) amount of heat will be released when this iron cools from 620 to 20 ° C.
So, to find the amount of heat necessary to heat the body or released by it during cooling, you need to multiply the specific heat of the body by its mass and by the difference between its final and initial temperatures: 
??? 1. Give examples showing that the amount of heat received by a body when heated depends on its mass and temperature changes. 2. By what formula is the amount of heat required to heat the body or released by it during cooling?
S.V. Gromov, N.A. Motherland, Physics Grade 8
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Assignment and answers from physics by class, download physics abstracts, planning physics lessons Grade 8, everything for the student to prepare for the lessons, lesson plan in physics, physics tests online, homework and work
Lesson content lesson summary support frame lesson presentation accelerative methods interactive technologies Practice tasks and exercises self-examination workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures graphics, tables, schemes humor, anecdotes, jokes, comics parables, sayings, crossword puzzles, quotes Add-ons abstracts articles chips for inquisitive cheat sheets textbooks basic and additional glossary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in the textbook elements of innovation in the lesson replacing obsolete knowledge with new ones Only for teachers perfect lessons calendar plan for the year methodological recommendations of the discussion program Integrated Lessons721. Why is water used to cool some mechanisms?
Water has a high specific heat capacity, which contributes to good heat removal from the mechanism.
722. In what case should more energy be expended: for heating one liter of water by 1 °C or for heating one hundred grams of water by 1 °C?
To heat a liter of water, since the larger the mass, the more energy needs to be expended.
723. Cupronickel and silver forks of the same mass were dipped into hot water. Do they receive the same amount of heat from water?
A cupronickel fork will receive more heat, because the specific heat of cupronickel is greater than that of silver.
724. A piece of lead and a piece of cast iron of the same mass were hit three times with a sledgehammer. Which part got hotter?
Lead will heat up more because its specific heat capacity is less than cast iron, and less energy is needed to heat the lead.
725. One flask contains water, the other contains kerosene of the same mass and temperature. An equally heated iron cube was thrown into each flask. What will heat up to a higher temperature - water or kerosene?
Kerosene.
726. Why are temperature fluctuations in winter and summer less sharp in cities on the seashore than in cities located inland?
Water heats up and cools down more slowly than air. In winter, it cools down and moves warm air masses on land, making the climate on the coast warmer.
727. The specific heat capacity of aluminum is 920 J/kg °C. What does this mean?
This means that it takes 920 J to heat 1 kg of aluminum by 1 °C.
728. Aluminum and copper bars of the same mass of 1 kg are cooled by 1 °C. How much will the internal energy of each block change? Which bar will change more and by how much?
729. What amount of heat is needed to heat a kilogram iron billet by 45 °C?
730. How much heat is required to heat 0.25 kg of water from 30°C to 50°C?
731. How will the internal energy of two liters of water change when heated by 5 °C?
732. How much heat is needed to heat 5 g of water from 20°C to 30°C?
733. What amount of heat is needed to heat an aluminum ball weighing 0.03 kg by 72 °C?
734. Calculate the amount of heat required to heat 15 kg of copper by 80 °C.
735. Calculate the amount of heat required to heat 5 kg of copper from 10 °C to 200 °C.
736. What amount of heat is required to heat 0.2 kg of water from 15 °C to 20 °C?
737. Water weighing 0.3 kg has cooled down by 20 °C. By how much is the internal energy of water reduced?
738. How much heat is needed to heat 0.4 kg of water at a temperature of 20 °C to a temperature of 30 °C?
739. How much heat is spent on heating 2.5 kg of water by 20 °C?
740. How much heat was released when 250 g of water cooled from 90 °C to 40 °C?
741. How much heat is required to heat 0.015 liters of water by 1 °C?
742. Calculate the amount of heat required to heat a pond with a volume of 300 m3 by 10 °C?
743. How much heat must be imparted to 1 kg of water in order to raise its temperature from 30°C to 40°C?
744. Water with a volume of 10 liters has cooled down from a temperature of 100 °C to a temperature of 40 °C. How much heat is released in this case?
745. Calculate the amount of heat required to heat 1 m3 of sand by 60 °C.
746. Air volume 60 m3, specific heat capacity 1000 J/kg °C, air density 1.29 kg/m3. How much heat is needed to raise it to 22°C?
747. Water was heated by 10 ° C, spending 4.20 103 J of heat. Determine the amount of water.
748. Water weighing 0.5 kg reported 20.95 kJ of heat. What was the temperature of the water if the initial temperature of the water was 20°C?
749. 8 kg of water at 10 °C is poured into a copper saucepan weighing 2.5 kg. How much heat is needed to bring the water to a boil in a saucepan?
750. A liter of water at a temperature of 15 ° C is poured into a copper ladle weighing 300 g. How much heat is needed to heat the water in the ladle by 85 ° C?
751. A piece of heated granite weighing 3 kg is placed in water. Granite transfers 12.6 kJ of heat to water, cooling by 10 °C. What is the specific heat capacity of the stone?
752. Hot water at 50°C was added to 5 kg of water at 12°C, obtaining a mixture with a temperature of 30°C. How much water was added?
753. Water at 20°C was added to 3 liters of water at 60°C to obtain water at 40°C. How much water was added?
754. What will be the temperature of the mixture if 600 g of water at 80°C are mixed with 200 g of water at 20°C?
755. A liter of water at 90°C was poured into water at 10°C, and the temperature of the water became 60°C. How much cold water was there?
756. Determine how much hot water heated to 60°C must be poured into a vessel if the vessel already contains 20 liters of cold water at a temperature of 15°C; the temperature of the mixture should be 40 °C.
757. Determine how much heat is required to heat 425 g of water by 20 °C.
758. How many degrees will 5 kg of water heat up if the water receives 167.2 kJ?
759. How much heat is required to heat m grams of water at a temperature t1 to a temperature t2?
760. 2 kg of water is poured into the calorimeter at a temperature of 15 °C. To what temperature will the water of the calorimeter heat up if a brass weight of 500 g heated to 100 °C is lowered into it? The specific heat capacity of brass is 0.37 kJ/(kg °C).
761. There are pieces of copper, tin and aluminum of the same volume. Which of these pieces has the largest and which the smallest heat capacity?
762. 450 g of water, the temperature of which is 20 °C, was poured into the calorimeter. When 200 g of iron filings heated to 100°C were immersed in this water, the temperature of the water became 24°C. Determine the specific heat capacity of sawdust.
763. A copper calorimeter weighing 100 g holds 738 g of water, the temperature of which is 15 °C. 200 g of copper was lowered into this calorimeter at a temperature of 100 °C, after which the temperature of the calorimeter rose to 17 °C. What is the specific heat capacity of copper?
764. A steel ball weighing 10 g is taken out of the furnace and lowered into water at a temperature of 10 °C. The water temperature rose to 25°C. What was the temperature of the ball in the oven if the mass of water is 50 g? The specific heat capacity of steel is 0.5 kJ/(kg °C).
770. A steel chisel weighing 2 kg was heated to a temperature of 800 °C and then lowered into a vessel containing 15 liters of water at a temperature of 10 °C. To what temperature will the water in the vessel be heated?
(Indication. To solve this problem, it is necessary to create an equation in which the desired temperature of the water in the vessel after the cutter is lowered is taken as the unknown.)
771. What temperature will water get if you mix 0.02 kg of water at 15 °C, 0.03 kg of water at 25 °C, and 0.01 kg of water at 60 °C?
772. Heating a well ventilated class requires an amount of heat of 4.19 MJ per hour. Water enters the heating radiators at 80°C and exits at 72°C. How much water should be supplied to the radiators every hour?
773. Lead weighing 0.1 kg at a temperature of 100 °C was immersed in an aluminum calorimeter weighing 0.04 kg containing 0.24 kg of water at a temperature of 15 °C. After that, the temperature of 16 °C was established in the calorimeter. What is the specific heat capacity of lead?
Outline plan
open physics lesson in 8 "E" class
MOU gymnasium No. 77, o. Tolyatti
physics teachers
Ivanova Maria Konstantinovna
Lesson topic:
Solving problems for calculating the amount of heat required to heat the body or released by it during cooling.
The date of the:
The purpose of the lesson:
to develop practical skills in calculating the amount of heat required for heating and released during cooling;
develop counting skills, improve logical skills in analyzing the plot of problems, solving qualitative and computational problems;
to cultivate the ability to work in pairs, respect the opinion of the opponent and defend their point of view, be careful when completing tasks in physics.
Lesson equipment:
computer, projector, presentation on the topic (Appendix No. 1), materials from a single collection of digital educational resources.
Lesson type:
problem solving.
“Put your finger into the flame from a match, and you will experience a sensation that is not equal in heaven or on earth; however, everything that has happened is simply the result of collisions of molecules.
J. Wheeler
During the classes:
Organizing time
Greeting students.
Checking for absent students.
Presentation of the topic and objectives of the lesson.
Checking homework.
1.Frontal survey
What is the specific heat capacity of a substance? (Slide #1)
What is the unit of specific heat capacity of a substance?
Why do bodies of water freeze slowly? Why doesn’t ice leave rivers and especially lakes for a long time, although the weather has been warm for a long time?
Why is it warm enough on the Black Sea coast of the Caucasus even in winter?
Why do some metals cool much faster than water? (Slide #2)
2. Individual survey (cards with multi-level tasks for several students)
Exploring a new topic.
1. Repetition of the concept of the amount of heat.
Quantity of heat- a quantitative measure of the change in internal energy during heat transfer.
The amount of heat absorbed by the body is considered to be positive, and the amount of heat released is negative. The expression “the body has a certain amount of heat” or “the body contains (stored) some amount of heat” does not make sense. The amount of heat can be received or given away in any process, but it cannot be possessed.
During heat exchange at the boundary between bodies, slowly moving molecules of a cold body interact with rapidly moving molecules of a hot body. As a result, the kinetic energies of the molecules are equalized and the velocities of the molecules of a cold body increase, while those of a hot body decrease.
During heat exchange, there is no conversion of energy from one form to another; part of the internal energy of a hot body is transferred to a cold body.
2. The formula for the amount of heat.
We derive a working formula to solve problems for calculating the amount of heat: Q = cm ( t 2 - t 1 ) - writing on the board and in notebooks.
We find out that the amount of heat given or received by the body depends on the initial temperature of the body, its mass and its specific heat capacity.
In practice, thermal calculations are often used. For example, when constructing buildings, it is necessary to take into account how much heat the entire heating system should give to the building. You should also know how much heat will go into the surrounding space through windows, walls, doors.
3 . The dependence of the amount of heat on various quantities . (Slides #3, #4, #5, #6)
4 . Specific heat (Slide number 7)
5. Units for measuring the amount of heat (Slide number 8)
6. An example of solving a problem for calculating the amount of heat (Slide number 10)
7. Solving problems for calculating the amount of heat on the board and in notebooks
We also find out that if heat exchange occurs between bodies, then the internal energy of all heating bodies increases by as much as the internal energy of cooling bodies decreases. To do this, we use an example of a solved problem from § 9 of the textbook.
Dynamic pause.
IV. Consolidation of the studied material.
1. Questions for self-control (Slide number 9)
2. Solving quality problems:
Why is it hot in deserts during the day, but at night the temperature drops below 0°C? (Sand has a low specific heat capacity, so it heats up and cools down quickly.)
A piece of lead and a piece of steel of the same mass were hit with a hammer the same number of times. Which piece got hotter? Why? (The piece of lead heated up more, because the specific heat capacity of lead is less.)
Why do iron stoves heat up a room faster than brick stoves, but do not stay warm for so long? (The specific heat capacity of copper is less than that of brick.)
Copper and steel weights of the same mass are given equal amounts of heat. Which weight will change the temperature the most? (At copper, because the specific heat capacity of copper is less.)
What consumes more energy: heating water or heating an aluminum pan, if their masses are the same? (For heating water, because the specific heat capacity of water is large.)
As you know, iron has a higher specific heat capacity than copper. Consequently, a stinger made of iron would have a greater supply of internal energy than the same sting made of copper, if their masses and temperatures are equal. Why, despite this, are soldering iron tips made of copper? (Copper has a high thermal conductivity.)
It is known that the thermal conductivity of metal is much greater than the thermal conductivity of glass. Why, then, are calorimeters made of metal and not glass? (The metal has a high thermal conductivity and low specific heat, due to which the temperature inside the calorimeter quickly equalizes, and little heat is spent on heating it. In addition, metal radiation is much less than glass radiation, which reduces heat loss.)
It is known that loose snow protects the soil well from freezing, because it contains a lot of air, which is a poor conductor of heat. But after all, even layers of air adjoin the soil that is not covered with snow. Why, then, does she not freeze much in this case? (The air, in contact with the soil not covered with snow, is constantly in motion, mixed. This moving air removes heat from the earth and increases the evaporation of moisture from it. The air, which is between the particles of snow, is inactive and, as a poor conductor of heat, protects the earth from freezing.)
3. Solution of calculation problems
The first two tasks are solved by highly motivated students at the blackboard with collective discussion. We find the right approaches in reasoning and solving problems.
Task #1.
When heating a piece of copper from 20°C to 170°C, 140,000 J of heat were expended. Determine the mass of copper.
Task #2
What is the specific heat capacity of a liquid if it took 150,000 J to heat 2 liters of it by 20 ° C. The density of the liquid is 1.5 g / cm³
Students answer the following questions in pairs:
Task number 3.
Two copper balls of mass m o and 4m o heated so that both balls receive the same amount of heat. At the same time, the large ball heated up by 5°C. How much did the ball of smaller mass heat up?
Task number 4.
How much heat is released when 4 m³ of ice is cooled from 10°C to -40°C?
Task number 5.
In which case will more heat be required to heat two substances if the heating of two substances is the same ∆ t 1 = ∆t 2 The first substance is a brick with a mass of 2 kg and s = 880 J / kg ∙ ° C, and brass - a mass of 2 kg and s \u003d 400 J / kg ∙ ° C
Task number 6.
A steel bar of mass 4 kg is heated. In this case, 200,000 J of heat were spent. Determine the final body temperature if the initial temperature is t 0 = 10°C
When students solve problems on their own, it is natural that questions arise. The most frequently asked questions are discussed collectively. Those questions that are of a private nature are given individual answers.
Reflection. Putting marks.
Teacher: So, guys, what did you learn in the lesson today and what did you learn new?
Sample student responses :
Worked out the skills of solving qualitative and computational problems on the topic "Calculation of the amount of heat required to heat the body and released during cooling."
We were convinced in practice how such subjects as physics and mathematics overlap and are connected.
Homework:
Solve problems No. 1024, 1025, from the collection of problems by V.I. Lukashik, E. V. Ivanova.
Independently come up with a problem for calculating the amount of heat required to heat the body or released by it during cooling.
« Physics - Grade 10 "
In what processes does aggregate transformation of matter occur?
How can the state of matter be changed?
You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
Thus, when forging a metal, work is done and it is heated, while at the same time the metal can be heated over a burning flame.
Also, if the piston is fixed (Fig. 13.5), then the volume of gas does not change when heated and no work is done. But the temperature of the gas, and hence its internal energy, increases.
Internal energy can increase and decrease, so the amount of heat can be positive or negative.
The process of transferring energy from one body to another without doing work is called heat exchange.
The quantitative measure of the change in internal energy during heat transfer is called amount of heat.
Molecular picture of heat transfer.
During heat exchange at the boundary between bodies, slowly moving molecules of a cold body interact with rapidly moving molecules of a hot body. As a result, the kinetic energies of the molecules are equalized and the velocities of the molecules of a cold body increase, while those of a hot body decrease.
During heat exchange, there is no conversion of energy from one form to another; part of the internal energy of a hotter body is transferred to a less heated body.
The amount of heat and heat capacity.
You already know that in order to heat a body with mass m from temperature t 1 to temperature t 2, it is necessary to transfer to it the amount of heat:
Q \u003d cm (t 2 - t 1) \u003d cm Δt. (13.5)
When the body cools, its final temperature t 2 turns out to be less than the initial temperature t 1 and the amount of heat given off by the body is negative.
The coefficient c in formula (13.5) is called specific heat capacity substances.
Specific heat- this is a value numerically equal to the amount of heat that a substance with a mass of 1 kg receives or gives off when its temperature changes by 1 K.
The specific heat capacity of gases depends on the process by which heat is transferred. If you heat a gas at constant pressure, it will expand and do work. To heat a gas by 1 °C at constant pressure, it needs to transfer more heat than to heat it at a constant volume, when the gas will only heat up.
Liquids and solids expand slightly when heated. Their specific heat capacities at constant volume and constant pressure differ little.
Specific heat of vaporization.
To convert a liquid into vapor during the boiling process, it is necessary to transfer a certain amount of heat to it. The temperature of a liquid does not change when it boils. The transformation of liquid into vapor at a constant temperature does not lead to an increase in the kinetic energy of molecules, but is accompanied by an increase in the potential energy of their interaction. After all, the average distance between gas molecules is much greater than between liquid molecules.
The value numerically equal to the amount of heat required to convert a 1 kg liquid into steam at a constant temperature is called specific heat of vaporization.
The process of liquid evaporation occurs at any temperature, while the fastest molecules leave the liquid, and it cools during evaporation. The specific heat of vaporization is equal to the specific heat of vaporization.
This value is denoted by the letter r and is expressed in joules per kilogram (J / kg).
The specific heat of vaporization of water is very high: r H20 = 2.256 10 6 J/kg at a temperature of 100 °C. In other liquids, such as alcohol, ether, mercury, kerosene, the specific heat of vaporization is 3-10 times less than that of water.
To convert a liquid of mass m into steam, an amount of heat is required equal to:
Q p \u003d rm. (13.6)
When steam condenses, the same amount of heat is released:
Q k \u003d -rm. (13.7)
Specific heat of fusion.
When a crystalline body melts, all the heat supplied to it goes to increase the potential energy of interaction of molecules. The kinetic energy of the molecules does not change, since melting occurs at a constant temperature.
The value numerically equal to the amount of heat required to transform a crystalline substance weighing 1 kg at a melting point into a liquid is called specific heat of fusion and are denoted by the letter λ.
During the crystallization of a substance with a mass of 1 kg, exactly the same amount of heat is released as is absorbed during melting.
The specific heat of melting of ice is rather high: 3.34 10 5 J/kg.
“If ice did not have a high heat of fusion, then in spring the entire mass of ice would have to melt in a few minutes or seconds, since heat is continuously transferred to ice from the air. The consequences of this would be dire; for even under the present situation great floods and great torrents of water arise from the melting of great masses of ice or snow.” R. Black, 18th century
In order to melt a crystalline body of mass m, an amount of heat is required equal to:
Qpl \u003d λm. (13.8)
The amount of heat released during the crystallization of the body is equal to:
Q cr = -λm (13.9)
Heat balance equation.
Consider heat exchange within a system consisting of several bodies initially having different temperatures, for example, heat exchange between water in a vessel and a hot iron ball lowered into water. According to the law of conservation of energy, the amount of heat given off by one body is numerically equal to the amount of heat received by another.
The given amount of heat is considered negative, the received amount of heat is considered positive. Therefore, the total amount of heat Q1 + Q2 = 0.
If heat exchange occurs between several bodies in an isolated system, then
Q 1 + Q 2 + Q 3 + ... = 0. (13.10)
Equation (13.10) is called heat balance equation.
Here Q 1 Q 2 , Q 3 - the amount of heat received or given away by the bodies. These quantities of heat are expressed by formula (13.5) or formulas (13.6) - (13.9), if various phase transformations of the substance occur in the process of heat transfer (melting, crystallization, vaporization, condensation).
(or heat transfer).
Specific heat capacity of a substance.
Heat capacity is the amount of heat absorbed by the body when heated by 1 degree.
The heat capacity of the body is indicated by a capital Latin letter With.
What determines the heat capacity of a body? 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 kind of substance? Let's do an experiment. Let's take two identical vessels and, pouring water weighing 400 g into one of them, and vegetable oil weighing 400 g into the other, we will begin to heat them with the help of identical burners. By observing the readings of thermometers, 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, to heat the same mass of different substances to the same temperature, different amounts of heat are required. The amount of heat required to heat a body and, consequently, its heat capacity depend on the kind of substance of which this body is composed.
So, for example, to increase the temperature of water with a mass of 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.
The physical quantity showing how much heat is required to heat 1 kg of a substance by 1 ºС is called specific heat this substance.
Each substance has its own specific heat capacity, which is denoted by the Latin letter c and is measured in joules per kilogram-degree (J / (kg ° C)).
The specific heat capacity of the same substance in different aggregate states (solid, liquid and gaseous) is different. For example, the specific heat capacity of water is 4200 J/(kg ºС), and the specific heat capacity of ice is 2100 J/(kg ºС); aluminum in the solid state has a specific heat capacity of 920 J/(kg - °C), and in the liquid state it is 1080 J/(kg - °C).
Note that water has a very high specific heat capacity. Therefore, the water in the seas and oceans, heating up in summer, absorbs a large amount of heat from the air. Due to this, in those places that are located near large bodies of water, summer is not as hot as in places far from water.
Calculation of the amount of heat required to heat the body or released by it during cooling.
From the foregoing, it is clear that the amount of heat necessary to heat the 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 temperature of the body.
So, to determine the amount of heat required to heat the body or released by it during cooling, you need to multiply the specific heat 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 is the specific heat capacity, m- body mass , t 1 - initial temperature, t 2 is the final temperature.
When the body is heated t 2 > t 1 and hence Q > 0 . When the body is cooled t 2and< t 1 and hence Q< 0 .
If the heat capacity of the whole body is known With, Q is determined by the formula:
Q \u003d C (t 2 - t 1 ) .
