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Hot coffee was poured into a cup. Porous brick will provide better thermal insulation of a building because voids filled with air have poor thermal conductivity (?) - Document. A. M. Shepelev how to build a rural house

Trufanova Olga Nikolaevna,

Physics teacher

municipal budgetary educational institution

municipal formation "City of Arkhangelsk"

"Secondary school No. 14"

PHYSICS IN THE KITCHEN.

Summary lesson on topics:

“Thermal phenomena”, “Changes in aggregate states of matter”

8th grade.

The purpose of the lesson is to create conditions for generalizing and systematizing students’ knowledge on the topics of the 8th grade physics course “Thermal Phenomena”, “Changes in Aggregate States of Matter”.

Educational objectives of the lesson

developing the ability to find the manifestation of thermal phenomena: thermal conductivity, convection, radiation, phase transitions in practical life;

formation of skills and abilities to apply acquired knowledge to explain thermal phenomena encountered in everyday life, to explain the principle of operation of technical devices and household items;

solving practical problems of everyday life.

Developmental objectives of the lessonrepresented by a set of actions of the student and teacher aimed at:

development of the ability to generalize learned facts

development of cognitive interest through the organization of gaming and competitive situations.

Educational objectives of the lessonrepresented by a set of actions of the student and teacher aimed at

showing the practical significance of thermal phenomena and processes in everyday life;

developing confidence in the possibility of knowing natural phenomena;

developing the skills to work in a group, present your arguments and explanations, and lead a discussion.

During the classes:

Organizational stage (2 minutes).

The kitchen is the most comfortable and functional room in the house: food is stored there, food is prepared, we have breakfast and lunch there, conversations are held there and secrets are shared...

At the same time kitchen appliances and accessories are constantly being modernized, although the kitchen is the oldest part of the home. How to explain this? I propose to consider this question from the perspective of a physicist and give an answer to it at the end of the lesson.

There are kitchen utensils on the teacher's table. On the slide:

What physical processes and phenomena can

found in the kitchen?

Let's start reasoning.

2. Main part (37 minutes).

Stage 1 of the conversation (up to 8 minutes). Question on the slide:" Who cares?"

Do we always think about how to use household items more correctly or more efficiently?

Which kettle cools down faster, matte aluminum or shiny chrome?

Thermoses are made with a flask covered with foam and with a vacuum layer. Which type of thermos is more efficient?

Why do you use wooden spoons and not metal ones when making jam?

Hot coffee was poured into a cup. What should you do to make the coffee cool faster: pour cold milk into it immediately or after a while?

In which cup, dark or white, will the water cool faster?

You need to cool the water. Do you place the pan on ice or put ice on the lid next to the water? Why?

Glasses often crack when hot water is poured into them. Which glass is more likely to crack, faceted or smooth?

Why do you put a spoon in a glass when you pour hot tea?

Why deal with scale in a kettle? What difference does it make: there is scale or not?

Let's summarize.

Stage 2 of the conversation (10 minutes). Question on the slide:"How it works?"

Does every family use these devices? How do they work? What are they needed for?

The students of the class prepared in advance mini-messages on each of the devices and devices. There is a request for speakers to prove the need for their use.

Pictures on the slides: 1. KITCHEN HOOD.

2. PRESSURE COOKER.

3. KITCHEN “KITCHEN”: A hot stand, an oven mitt, a “warmer” for a kettle (pan). What do they have in common?

Let's summarize.

Stage 3 of the conversation (up to 9 minutes). On the slide:“About products and their preparation”

Is it possible to apply physical knowledge when preparing dishes?

To make soup quickly, which pan will you choose?

(Analyze each selected option with teams)

What causes the lid of a saucepan to jump when water boils?

Why is it not necessary to stir soup while cooking, but semolina porridge must be stirred constantly?

Why do potatoes take longer to cook in water than in a steamer at the same temperature?

Once boiled water does not boil as violently as raw water. Why?

Why doesn’t an egg taken from boiling water burn your hands?

What causes milk to sour?

Why does the length of time it takes to cook meat until done does not depend on whether the broth is boiling over high or low heat?

Why does butter sometimes foam when you want to melt it in a hot frying pan?

To prepare croutons, cut the bread into thin slices or small cubes, place it in a slightly heated frying pan or on a baking sheet and put it in the oven. Why do they do this?

Let's summarize.

Stage 4 of the conversation (10 minutes). On the slide:“Let’s make a menu”

Creative task.

When you work, you waste your internal energy. How do you replenish it?

The guys are united in groups of 4 people. The group is given 5 minutes to work on the task. Draw up the menu and daily routine on A1 sheets. Then the menu is “protected” by each group. (The sheets are attached to a magnetic board).

Using two tables: energy costs and caloric content of food products, create a student’s menu for 1 day. Choose the conditions of your daily routine yourself. At the end of the work, answer the question: “Will food replenish energy costs for the day?”

(Students are offered a table of energy consumption. Approximate content: (for 1 hour per 1 kg of human weight) when preparing lessons - 9000 J; when charging - 16000 J; when lying - 4000 J; when swimming - 30000 J; while sleeping - 4000 J; when walking - 15000 J.

A table of food calorie content is provided. For convenience, energy units kcal should be converted to J/g in advance. For example: bread – 9000J/g; sugar – 17150 J/g; milk – 3000J/g; meat – 7500J/g; potatoes – 4000J/g; oil – 33000J/g; vegetables and fruits – 600 – 2000 J/g; eggs – 7000J/g).

Let's summarize.

3. Generalization, summing up the work, homework (6 minutes).

Key question:“What did you take note from the lesson? What is a person doing in the kitchen? Why are kitchen appliances and accessories constantly being modernized, although the kitchen is the oldest part of the home?

Homework:Conduct independent theoretical or practical research on the topic: “Does the water in tubular pasta boil when cooked?”


TYPES OF HEAT TRANSFER.

Enough level

1. Which of the following substances have good thermal conductivity:
copper, air, aluminum, water, glass, water vapor?

Answer: copper and aluminum have good thermal conductivity

2. Which of the following substances have poor thermal conductivity:
cardboard, iron, rubber, steel, paper?

Answer: they have poor thermal conductivity: cardboard, rubber, paper

3. Hot water is poured into aluminum and glass pans of equal capacity.
Which pan will heat up faster to the temperature of the water poured into it?

Answer: An aluminum pan will heat up faster because
that it has greater thermal conductivity

4. Will regular or porous brick provide better thermal insulation for a building?
porous brick will provide better thermal insulation of the building because
that voids filled with air have poor thermal conductivity (?)

5. Which shoes make your feet feel colder in winter: loose or tight ones?

Answer: tight, because there is no air gap in it,
with low thermal conductivity

6. Which type of heat transfer plays the main role in heating water in a kettle,
standing on the stove?

Answer: the main role in heating water in a kettle convection plays

7. It is necessary to cool the water poured into the tank faster.
Is it better to put the tank on ice or put ice on the lid of the tank?
Answer:in order to quickly cool the water poured into the tank,
You need to put ice on the tank lid
During convection, warm layers of water rise upward
upon contact with a cold lid they cool down (?)

8. Which dress is less hot in summer: light or dark?

Answer: in a light dress it is less hot in summer because
that it absorbs less solar energy,
transmitted by radiation

9. Which soils, under the same conditions, warm up more strongly in the sun -
podzolic or chernozem?

Answer: Chernozem soils warm up more strongly in the sun because
that they absorb more energy from the sun's rays

10. Keep tea hot in a thermos. Is it possible to preserve cold fruit juice in it?

Average level

1. Why are the handles of taps on hot water tanks made of wood?

Answer: tap handles for hot water tanks are made of wood because
that they have poor thermal conductivity

2. In summer, ice is stored under a layer of sawdust and earth. Why?

Answer: in summer, ice is stored under a layer of sawdust and earth because
that they have poor thermal conductivity

3. In what case will a piece of ice brought into the room melt faster:
when will they simply put it on the table or when will they cover it with a woolen scarf on top?

Answer:A piece of ice brought into the room will melt faster when it is simply placed on the table(?)

4. Why are fuel storage tanks painted with “silver” paint at oil depots?

Answer:At oil depots, fuel storage tanks are painted with “silver” paint because
that light-colored surfaces do not heat up well under the influence of radiation(?)

5. Why are heating radiators indoors located near the floor and not near the ceiling?

Answer: cold air entering through the window is heavier than warm air,
and so it goes down, where it is heated by the central heating radiator

6. Which bodies - solids, liquids or gases - have the lowest thermal conductivity? Why?

Answer:Gases have the lowest thermal conductivity because
that gas molecules are located at a great distance from each other
and interact poorly (?)

7. Where should you keep a thermometer to determine air temperature -
in the shade or in the sun?
Answer:To determine the air temperature, the thermometer must be kept in the shade because
What… (?)

8. What will cool down faster: a glass of compote or a glass of jelly? Why?

Answer:a glass of compote will cool faster because
that there is less mutual attraction between molecules in it
and convection occurs faster (?)

9. Why do plants in lowlands die from frost more often than at higher elevations?

Answer:cold air is heavier than warm air and therefore sinks
in the lowlands on a cloudless night it is colder than in the higher elevations (?)

10. Why does snow melt faster in the city in spring than in the field?

Answer:In spring the snow in the city melts faster because buildings warm up well under the influence of solar radiation and transfer part of their energy to the snow(?)

High level

1. Which bodies - solid, liquid or gaseous - have the best thermal conductivity?

Answer:Solids have better thermal conductivity because
that their molecules are at a small distance from each other
and interact well (?)

2. In what bodies - liquids, solids, gases - is convection observed? Why?

Answer:convection is observed in liquids and gases because
that in them the mutual attraction between molecules is less and the molecules can move freely (?)

3. At what temperature will both metal and wood feel equally hot to the touch?

Answer: both metal and wood will feel equally hot to the touch at a temperature of 36.6 0 C because at this temperature there will be no heat exchange (?)

4. It is necessary to quickly cool the bottle of lemonade. Where should the bottle be placed for this: in the snow or in crushed ice, if their temperature is the same?

Answer: in order to quickly cool a bottle of lemonade, it must be placed in crushed ice, which has greater thermal conductivity, so the heat exchange will go faster (?)

5.When is it more convenient for sailing ships to enter the harbor - during the day or at night?

Answer: It is more convenient for sailing ships to enter the harbor during the day, when the land is warmed up faster by the sun, the heated air rises, and is replaced, from the side of the sea, by a stream of cold air - the daytime breeze (?)

6. Hot coffee was poured into the cup. What should you do to make the coffee cool faster: pour milk into it immediately or after a while?

Answer:to make hot coffee cool faster milk must be poured into it after some time
a film forms on the surface of the coffee, which has poor thermal conductivity(?)

7. Which factory pipes are better: iron or brick?

Answer:brick factory pipes are better because
that they have poor thermal conductivity
at the top of the pipe are surrounded by a layer of cold air,
so the traction in a brick pipe is better(?)

8. When is draft in pipes better - in winter or summer? Why?
Answer: draft in pipes is better in winter because
What …(?)

9. Why do window panes begin to freeze from below and to a greater extent than from above?

Answer:cold air is heavier than warm air and therefore it sinks down(?)

10. Will a candle burn on board the space orbital complex?

Answer: no, because convection is carried out due to the Archimedes force,
which does not occur in a state of weightlessness

11. Why do we feel warmer in a room at a temperature of 20°C?
than in water at a temperature of 25°C?

Answer:The thermal conductivity of water is greater, so heat exchange occurs faster in it,
body temperature drops quickly (?)

12. Why do many animals sleep curled up in a ball in cold weather?

Answer:The smaller the surface area of ​​an animal's body, the less heat it generates.
gives away to the air around him(?)

13. Why is the highest air temperature not at noon, but in the afternoon?

Answer:During the day, the land surface becomes very hot due to solar radiation.
and in the afternoon heats the air by convection(?)

14. On a hot day, the dry thermometer shows 35°C.
Will the thermometer readings change if a fan is turned on next to it?
Consider two cases: a) the thermometer is in the shade; b) the thermometer is illuminated by the sun.

Answer: if on a hot day the dry thermometer is in the shade and the air flow from a fan is directed at it, then its temperature will not change

If on a hot day the dry thermometer is illuminated by the sun and a flow of air from a fan is directed at it, then its temperature will decrease because convection occurs faster (?)

15. How to set up a greenhouse? Why is the air temperature inside greenhouses higher than outside?

Answer: Greenhouses are used to protect plants from frost.
Glass frames allow solar radiation to pass through well. During the day the soil warms up.
At night, the greenhouse prevents warm air from moving upward. Therefore, the temperature in the greenhouse is higher than in the surrounding area.

Additionally:

1.For what purpose is the face sometimes lubricated with a thick cream in winter when it’s very cold?

2.The longer an enamel kettle is in use, the slower the water boils in it. Why?

3. Why do locals in Central Asian countries wear papa hats and cotton robes during extreme heat?

4. Why is the frost stronger on clear winter nights than on cloudy weather?

4. If a clear night is expected in spring or autumn, gardeners build fires that produce a lot of smoke,
enveloping plant. For what?

5. There is a known case when a parachutist with an open parachute, instead of going down, went up. How could this happen?

6. Using a thermal imager (night vision device), you can detect various bodies,
even slightly heated, regardless of whether these bodies are illuminated or are in complete darkness. What physical phenomenon is used in these devices?

7. In what case will a heated part cool faster: if it is placed on a wooden stand
or on a steel plate?

8. Which areas of the earth’s surface heat up more strongly in sunny weather:
plowed field or green meadow, dry or moist soil? Why?

9. Why does it feel cold even from well-sealed windows in winter?

10. In which kettle – white or dark – will water boil faster?

11. Why is there more draft in furnaces with high pipes than in furnaces with low pipes?

12. Why does a stone floor seem colder than a wooden floor in the same room?

13. Why do experienced housewives prefer to fry in cast iron pans?
and not on aluminum ones?

14. Which type of heat transfer is accompanied by the transfer of matter?

15. Why is the highest temperature not at noon, but in the afternoon?

16. The Earth continuously radiates energy into outer space. Why doesn't the Earth freeze?

17. In what case is energy transmitted by radiation? Explain with an example.

18. Why do aspen leaves sway in calm weather?

19. Why does a thin plastic film protect the plant from the night cold?

20. Why, when the stove starts heating up in the room,
is there a decrease in temperature? what... and purpose, That's why What temperature air at floor level...

  • A. M. Shepelev how to build a rural house

    Document

    ... - thermal insulation; ... porous brick ... bricks, better iron ore. Badly burned brick ... emptiness(air bags), reducing its mass and thermal conductivity. For monolithic one-story walls buildings ... provide the best ... That's why What it gets sucked into these cracks air ...

  • Question Composition of the installation process. Classification of methods

    Document

    ... , What glass is thermally conductive material... layers, filled out dehydrated air. Double-glazed windows have tall... buildings and structures. They must be connected to railway tracks and provided supply of compressed electricity air ...

  • The life of a modern person is unthinkable without sophisticated technology. Even in his home, he is surrounded by many instruments and devices, most of which require

    Document

    ... has good electrical conductivity, thermal conductivity, 3.5 times lighter than copper. On air... power sources. Because What really effective protection... buildings over 80% of the time. Modern houses often have good sound and thermal insulation ...

  • Enough level

    1. Which of the following substances have good thermal conductivity:
    copper, air, aluminum, water, glass, water vapor?

    Answer: copper and aluminum have good thermal conductivity

    2. Which of the following substances have poor thermal conductivity:


    cardboard, iron, rubber, steel, paper?

    Answer: they have poor thermal conductivity: cardboard, rubber, paper

    3. Hot water is poured into aluminum and glass pans of equal capacity.


    Which pan will heat up faster to the temperature of the water poured into it?

    Answer: An aluminum pan will heat up faster because
    that it has greater thermal conductivity

    4. Will regular or porous brick provide better thermal insulation for a building?


    porous brick will provide better thermal insulation of the building because
    that voids filled with air have poor thermal conductivity (?)

    5. Which shoes make your feet feel colder in winter: loose or tight ones?

    Answer: tight, because there is no air gap in it,
    with low thermal conductivity

    6. Which type of heat transfer plays the main role in heating water in a kettle,


    standing on the stove?

    Answer: the main role in heating water in a kettle convection plays

    7. It is necessary to cool the water poured into the tank faster.


    Is it better to put the tank on ice or put ice on the lid of the tank?
    Answer:in order to quickly cool the water poured into the tank,
    You need to put ice on the tank lid
    During convection, warm layers of water rise upward
    upon contact with a cold lid they cool down (?)

    8. Which dress is less hot in summer: light or dark?

    Answer: in a light dress it is less hot in summer because
    that it absorbs less solar energy,
    transmitted by radiation

    9. Which soils, under the same conditions, warm up more strongly in the sun -


    podzolic or chernozem?

    Answer: Chernozem soils warm up more strongly in the sun because
    that they absorb more energy from the sun's rays

    10. Keep tea hot in a thermos. Is it possible to preserve cold fruit juice in it?

    Average level

    1. Why are the handles of taps on hot water tanks made of wood?

    Answer: tap handles for hot water tanks are made of wood because

    2. In summer, ice is stored under a layer of sawdust and earth. Why?

    Answer: in summer, ice is stored under a layer of sawdust and earth because
    that they have poor thermal conductivity

    3. In what case will a piece of ice brought into the room melt faster:


    when will they simply put it on the table or when will they cover it with a woolen scarf on top?

    Answer: a piece of ice brought into the room will melt faster when it is simply placed on the table(?)

    4. Why are fuel storage tanks painted with “silver” paint at oil depots?

    Answer: at oil depots, fuel storage tanks are painted with “silver” paint because
    that light-colored surfaces do not heat up well under the influence of radiation(?)

    5. Why are heating radiators indoors located near the floor and not near the ceiling?

    Answer: cold air entering through the window is heavier than warm air,
    and so it goes down, where it is heated by the central heating radiator

    6. Which bodies - solids, liquids or gases - have the lowest thermal conductivity? Why?

    Answer: gases have the lowest thermal conductivity because
    that gas molecules are located at a great distance from each other
    and interact poorly (?)

    7. Where should you keep a thermometer to determine air temperature -


    in the shade or in the sun?
    Answer:To determine the air temperature, the thermometer must be kept in the shade because
    What… (?)

    8. What will cool down faster: a glass of compote or a glass of jelly? Why?

    Answer: a glass of compote will cool faster because
    that there is less mutual attraction between molecules in it
    and convection occurs faster (?)

    9. Why do plants in lowlands die from frost more often than at higher elevations?

    Answer: cold air is heavier than warm air and therefore sinks
    in the lowlands on a cloudless night it is colder than in the higher elevations (?)

    10. Why does snow melt faster in the city in spring than in the field?

    Answer:In spring the snow in the city melts faster because buildings warm up well under the influence of solar radiation and transfer part of their energy to the snow(?)

    High level

    1. Which bodies - solid, liquid or gaseous - have the best thermal conductivity?

    Answer: solids have better thermal conductivity because
    that their molecules are at a small distance from each other
    and interact well (?)

    2. In what bodies - liquids, solids, gases - is convection observed? Why?

    Answer: convection is observed in liquids and gases because
    that in them the mutual attraction between molecules is less and the molecules can move freely (?)

    3. At what temperature will both metal and wood feel equally hot to the touch?

    Answer: both metal and wood will feel equally hot to the touch at a temperature of 36.6 0 C because at this temperature there will be no heat exchange (?)

    4. It is necessary to quickly cool the bottle of lemonade. Where should the bottle be placed for this: in the snow or in crushed ice, if their temperature is the same?

    Answer: in order to quickly cool a bottle of lemonade, it must be placed in crushed ice, which has greater thermal conductivity, so heat transfer will occur faster (?)

    5. When is it more convenient for sailing ships to enter the harbor - during the day or at night?

    Answer: it is more convenient for sailing ships to enter the harbor during the day, when the land is warmed up faster by the sun, the heated air rises, and is replaced, from the side of the sea, by a stream of cold air - the daytime breeze (?)

    6. Hot coffee was poured into the cup. What should you do to make the coffee cool faster: pour milk into it immediately or after a while?

    Answer:to make hot coffee cool faster milk must be poured into it after some time
    a film forms on the surface of the coffee, which has poor thermal conductivity(?)

    7. Which factory pipes are better: iron or brick?

    Answer: brick factory pipes are better because
    that they have poor thermal conductivity
    at the top of the pipe are surrounded by a layer of cold air,
    so the traction in a brick pipe is better(?)

    8. When is draft in pipes better - in winter or summer? Why?


    Answer: draft in pipes is better in winter because
    What …(?)

    9. Why do window panes begin to freeze from below and to a greater extent than from above?

    Answer: cold air is heavier than warm air and therefore it sinks down(?)

    10. Will a candle burn on board the space orbital complex?

    Answer: no, because convection is carried out due to the Archimedes force,
    which does not occur in a state of weightlessness

    11. Why do we feel warmer in a room at 20°C?


    than in water at a temperature of 25°C?

    Answer: the thermal conductivity of water is greater, so heat exchange occurs faster in it,
    body temperature drops quickly (?)

    12. Why do many animals sleep curled up in a ball in cold weather?

    Answer: the smaller the surface area of ​​an animal's body, the less heat it generates.
    gives away to the air around him(?)

    13. Why is the highest air temperature not at noon, but in the afternoon?

    Answer: During the day, the land surface becomes very hot under the influence of solar radiation.
    and in the afternoon heats the air by convection(?)

    14. On a hot day, the dry thermometer shows 35°C.


    Will the thermometer readings change if a fan is turned on next to it?
    Consider two cases: a) the thermometer is in the shade; b) the thermometer is illuminated by the sun.

    Answer: if on a hot day the dry thermometer is in the shade and the air flow from a fan is directed at it, then its temperature will not change

    If on a hot day the dry thermometer is illuminated by the sun and a flow of air from a fan is directed at it, then its temperature will decrease because convection occurs faster (?)

    15. How to set up a greenhouse? Why is the air temperature inside greenhouses higher than outside?

    Answer: Greenhouses are used to protect plants from frost.
    Glass frames allow solar radiation to pass through well. During the day the soil warms up.
    At night, the greenhouse prevents warm air from moving upward. Therefore, the temperature in the greenhouse is higher than in the surrounding area.

    Additionally:


    1.For what purpose is the face sometimes lubricated with a thick cream in winter when it’s very cold?

    2.The longer an enamel kettle is in use, the slower the water boils in it. Why?

    3. Why do locals in Central Asian countries wear papa hats and cotton robes during extreme heat?

    4. Why is the frost stronger on clear winter nights than on cloudy weather?

    4. If a clear night is expected in spring or autumn, gardeners build fires that produce a lot of smoke,
    enveloping plant. For what?

    5. There is a known case when a parachutist with an open parachute, instead of going down, went up. How could this happen?

    6. Using a thermal imager (night vision device), you can detect various bodies,
    even slightly heated, regardless of whether these bodies are illuminated or are in complete darkness. What physical phenomenon is used in these devices?

    7. In what case will a heated part cool faster: if it is placed on a wooden stand


    or on a steel plate?

    8. Which areas of the earth’s surface heat up more strongly in sunny weather:


    plowed field or green meadow, dry or moist soil? Why?

    9. Why does it feel cold even from well-sealed windows in winter?

    10. In which kettle – white or dark – will water boil faster?

    11. Why is there more draft in furnaces with high pipes than in furnaces with low pipes?

    12. Why does a stone floor seem colder than a wooden floor in the same room?

    13. Why do experienced housewives prefer to fry in cast iron pans?


    and not on aluminum ones?

    14. Which type of heat transfer is accompanied by the transfer of matter?

    15. Why is the highest temperature not at noon, but in the afternoon?

    16. The Earth continuously radiates energy into outer space. Why doesn't the Earth freeze?

    17. In what case is energy transmitted by radiation? Explain with an example.

    18. Why do aspen leaves sway in calm weather?

    19. Why does a thin plastic film protect the plant from the night cold?

    20. Why, when the stove starts heating up in the room,


    Is there a drop in temperature?

    Coffee with cream April 23rd, 2012

    Which do you think will cool down faster: (1) a cup of hot coffee to which a portion of cream is immediately added, or (2) a cup of coffee that cools without cream, and exactly the same amount of cream is added later? Numerical example: coffee 250 g, cream added 60 g, cream temperature 6 degrees. The initial temperature of the coffee is 83 degrees, the room temperature is 22 degrees. We wait 15 minutes, which cup has the lower temperature?



    Simple model (Newton-Richmann law): the cooling rate is proportional to the temperature difference, that is, T"(t)= c(T-Tv), where Tv is the air temperature, and all physical properties (interface area, liquid heat capacity, etc.) are packaged into a constant c. Moreover, this magic constant also does not depend on the coffee/cream ratio. Solution: Coffee cools exponentially, then we need to take into account the proportional contribution of cream. In this model, adding cold cream slows down the cooling rate and (2) will cool down faster . In other words, the contribution of cream (to the sudden drop in temperature) is different when the coffee is hot and when it has already cooled down (see graphs in the comments).

    Formula for a numerical example: the temperature of coffee without cream drops as T(t)=22+61exp(-ct). (see in comments bitoff ).

    A coffee cooling table has been found in the literature, from which the constant can be determined c(see in comments). However, the data does not fit the exponential well, which raises questions about the accuracy of the measurements, as well as the accuracy of the model. The temperature measurement error in the table is indicated as 0.1 degrees, and the estimate of the temperature difference of the liquid in the cups according to the conditions of the numerical example gives 1-2 degrees.

    UPDATE (27/4-29/4). About the scope of applicability of the model: Experimental measurements may show an even larger difference than the model predicts!


    Data from an experiment on cooling coffee (table from the book by Gould, Tobochnik “Computer Modeling in Physics”, M. Mir, 1990, p. 35):

    1. comparison of measurement results from the table with the exponential model: Conclusion: the experimental data from the book does not fit so badly with the exponential model, with the exception of the first two or three points. Starting from the fourth point, the deviation is less than one degree.

    Practical tips:
    1. If you want to cool your coffee as quickly as possible: pour into a metal cup with thin walls, place in cold water and stir. Then add cream.
    2. If, on the contrary, you want to keep the coffee hot for as long as possible: preheat the thermos (especially with a metal flask), pour coffee into it right up to the stopper, and close it immediately.

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