Samacheer Kalvi Class 6 Science Solutions Term 2 Chapter 1 Heat

I. Choose The Correct Answer:

 

Question 1. When an object is heated, the molecules that make up the object
(a) begin to move faster
(b) lose energy
(c) become heavier
(d) become lighter
Answer: (a) begin to move faster
In simple words: When things get warm, the tiny parts inside them, called molecules, start to shake and move around more quickly. This added movement is what we feel as heat.

🎯 Exam Tip: Remember that heat is a form of energy, and energy causes particles to move. Increased molecular motion is a key indicator of higher temperature.

 

Question 2. The unit of heat is
(a) newton
(b) joule
(c) volt
(d) Celsius
Answer: (b) joule
In simple words: Just like we use meters for length, the Joule is the standard way to measure how much heat energy there is. It's a unit for all kinds of energy.

🎯 Exam Tip: It's crucial to distinguish between units of heat (energy) and units of temperature. Joule is for energy, Celsius/Kelvin for temperature.

 

Question 3. One litre of water at 30°C is mixed with one litre of water at 50°C. The temperature of the mixture will be
(a) 80°C
(b) More than 50°C but less than 80°C
(c) 20°C
(d) around 40°C
Answer: (d) around 40°C
In simple words: When you mix two equal amounts of water at different temperatures, the final temperature will be somewhere in the middle. It averages out the two temperatures.

🎯 Exam Tip: When mixing liquids of the same type and volume but different temperatures, the final temperature is roughly the average of the initial temperatures. For different volumes or specific heats, a weighted average calculation would be needed.

 

Question 4. An iron ball at 50°C is dropped in a mug containing water at 50°C. The heat will
(a) flow from iron ball to water.
(b) not flow from iron ball to water or from water to iron ball.
(c) flow from water to iron ball.
(d) increase the temperature of both.
Answer: (b) not flow from iron ball to water or from water to iron ball.
In simple words: Heat only moves from warmer things to cooler things. If both the iron ball and the water are at the same temperature, there is no temperature difference, so no heat will move between them.

🎯 Exam Tip: Heat transfer requires a temperature difference. If objects are at the same temperature, they are in thermal equilibrium, and no net heat flows between them.

II. Fill In The Blanks

 

Question. Fill in the blanks with the correct words.
1. Heat flows from a __________ body to a __________ body.
2. The hotness of the object is determined by its __________.
3. The SI unit of temperature is __________.
4. Solids __________ on heating and __________ on cooling.
5. Two bodies are said to be in the state of thermal __________ if there is no transfer of heat taking place.
Answer:
1. hot, cold
2. temperature
3. Kelvin
4. expand, contract
5. equilibrium
In simple words: Heat always moves from a hot place to a cold place. Temperature tells us how hot or cold something is, and Kelvin is the standard unit for it. Materials get bigger when hot and shrink when cold. When two things are the same temperature, they are balanced, and no heat moves.

🎯 Exam Tip: Pay attention to keywords like 'SI unit' for precise answers and understand the basic definitions for concepts like heat flow and thermal equilibrium.

III. True Or False. If False, Give The Correct Answer.

 

Question. State whether the following statements are True or False. If false, provide the correct statement.
1. Heat is a kind of energy that flows from a hot body to a cold body.
2. Steam is formed when heat is released from water.
3. Thermal expansion is always a nuisance.
4. Borosilicate glass do not expand much on being heated.
5. The unit of heat and temperature are the same.
Answer:
1. True
2. False - Steam is formed when heat is absorbed from the water.
3. False - Thermal expansion is not always a nuisance.
4. True
5. False – The units of heat and temperature are different.
In simple words: Heat is energy moving from hot to cold. Water needs to take in heat to turn into steam. While expansion can be a problem sometimes, it's also useful in many ways. Special glass like borosilicate doesn't expand much when heated. Heat is measured in Joules, but temperature is measured in units like Celsius or Kelvin; they are not the same.

🎯 Exam Tip: For False statements, always remember to write the correct reason or corrected statement to earn full marks. Understanding the difference between heat and temperature is fundamental.

IV. Give Reasons For The Following

 

Question 1. An ordinary glass bottle cracks when boiling water is poured into it, but a borosilicate glass bottle does not.
Answer: An ordinary glass bottle cracks because it expands unevenly when hot water is poured in. The inside part heats up and expands quickly, but the outside stays cool and doesn't expand as much. This difference in expansion causes stress, leading to cracks. Borosilicate glass, however, does not expand much when heated, so it can handle the sudden change in temperature without cracking. It's designed to resist thermal shock better.
In simple words: Normal glass breaks because it expands too quickly on the inside when hot water hits it, while the outside stays cold. Borosilicate glass does not expand as much, so it does not break.

🎯 Exam Tip: Mentioning "uneven expansion" and "low thermal expansion" for borosilicate glass are key points when explaining this phenomenon.

 

Question 2. The electric wire which sag in summer become straight in winter.
Answer: During summer, electric wires get hot due to the high ambient temperature and the current passing through them. This heat causes thermal expansion, making the wires lengthen and sag more. In winter, the temperature drops, causing the wires to contract and shorten, which makes them appear straighter. This is why power lines are installed with some sag.
In simple words: Wires get longer and sag in summer because of heat (thermal expansion). In winter, they get cold and shrink (contract), so they become straight again.

🎯 Exam Tip: Clearly state that wires expand in summer (heat) and contract in winter (cold) to show understanding of thermal expansion and contraction.

 

Question 3. Rivet is heated before fixing in the hole to join two metal plates.
Answer: Rivets are heated before being used to join two metal plates. When a rivet is heated, it undergoes thermal expansion, meaning it expands in size and becomes slightly softer. This makes it easier to pass through the holes in the metal plates. Once it's in place, one end is hammered to form a new head. As the hot rivet cools down, it contracts and shrinks. This contraction pulls the two metal plates tightly together, forming a very strong and secure joint.
In simple words: Rivets are heated so they expand and become soft, making them easy to put through holes. When they cool down, they shrink and pull the metal plates very tightly together.

🎯 Exam Tip: Highlight "expansion when hot" and "contraction when cold" as the reasons for the rivet's effective joining action.

V. Match The Following

 

Question. Match the following terms with their definitions or associated values.

Answer:
1. - e (Heat: Joule)
2. - c (Temperature: Kelvin)
3. - d (Thermal Equilibrium: No heat flow)
4. - a (Ice cube: 0° C)
5. - b (Boiling water: 100° C)
In simple words: Heat is measured in Joules. Temperature can be measured in Kelvin. Thermal equilibrium means no heat is moving. Ice melts at 0°C, and water boils at 100°C.

🎯 Exam Tip: Be sure to know the standard units for different physical quantities and the specific temperatures for phase changes of water.

VI. Analogy

 

Question. Complete the following analogies.
1. Heat: Joule :: Temperature : __________
2. Ice cube : 0°C :: Boiling water : __________
3. Total Kinetic Energy of molecules: Heat:: Average Kinetic Energy : __________
Answer:
1. Kelvin
2. 100° C
3. Temperature
In simple words: Heat is measured in Joules, just like temperature is measured in Kelvin. An ice cube is at 0°C, and boiling water is at 100°C. Total movement energy of molecules is heat, while the average movement energy is temperature.

🎯 Exam Tip: Analogies test your understanding of relationships. For heat and temperature, remember one is total energy and the other is average energy per particle.

VII. Give Very Short Answer:

 

Question 1. Make a list of electrical types of equipment at home from which we get heat.
Answer: Common electrical equipment at home that produces heat includes a water heater, iron box, electric kettle, and microwave oven. Many other devices like toasters, hair dryers, and electric heaters also work by converting electricity into heat.
In simple words: Things like water heaters, irons, electric kettles, and microwaves use electricity to make heat in our homes.

🎯 Exam Tip: List everyday appliances that clearly convert electrical energy into heat energy, avoiding those where heat is a byproduct rather than the primary function.

 

Question 2. What is the temperature?
Answer: Temperature is a measure of the degree of hotness or coldness of a substance. It indicates the average kinetic energy of the molecules within the substance. When molecules move faster, the temperature is higher.
In simple words: Temperature tells us how hot or cold something is. It shows how fast the tiny particles inside an object are moving.

🎯 Exam Tip: Define temperature in terms of "degree of hotness or coldness" and its relation to "average kinetic energy of molecules."

 

Question 3. What is thermal expansion?
Answer: Thermal expansion is the tendency of matter to change in volume, density, shape, or length in response to a change in temperature. When a substance is heated, its particles vibrate more, push each other further apart, and take up more space, causing it to expand.
In simple words: Thermal expansion is when a material gets bigger when it is heated up. The heat makes its tiny parts move more and spread out.

🎯 Exam Tip: The core idea of thermal expansion is that objects expand when heated, so ensure this key relationship is clearly stated in your definition.

 

Question 4. What do you understand by thermal equilibrium?
Answer: Thermal equilibrium is a state where two objects in thermal contact no longer exchange heat energy. This happens when both objects reach the same temperature. At this point, there is no net flow of heat from one object to the other.
In simple words: Thermal equilibrium means two things touching each other have reached the same temperature, so no more heat moves between them. They are in balance.

🎯 Exam Tip: Emphasize "no net transfer of heat" and "same temperature" when defining thermal equilibrium.

VIII. Give Short Answer:

 

Question 1. What difference do you think heating the solid will make in their molecules?
Answer:
1. When we heat solids, the vibrations and movement of molecules will increase.
2. The temperature of the object increases.
3. The distance between molecules will increase.
As a solid gets hotter, its particles gain energy and vibrate more intensely in their fixed positions, leading to an overall expansion of the material.
In simple words: When a solid is heated, its tiny particles vibrate faster and move more. This makes the solid hotter and causes the particles to spread out, making the solid expand.

🎯 Exam Tip: Focus on the three main effects: increased vibration/movement, increased temperature, and increased intermolecular distance, which leads to expansion.

 

Question 2. Distinguish between heat and temperature.

Answer:
Heat is the total amount of kinetic energy from all molecules in a substance, and it depends on the mass and number of molecules. Temperature, on the other hand, measures the average kinetic energy of the molecules, indicating how hot or cold something is. The SI unit for heat is the Joule, while for temperature, it is Kelvin. Heat can flow from one object to another, but temperature is a property of a single object.
In simple words: Heat is the total energy of all particles in an object. Temperature is how fast the particles are moving on average. Heat depends on size, but temperature does not. Heat is measured in Joules, and temperature in Kelvin.

🎯 Exam Tip: Clearly state that heat is total energy, while temperature is average kinetic energy. Remembering their SI units is also key for distinguishing them.

IX. Answer In Detail:

 

Question 1. Explain thermal expansion with suitable examples.
Answer: Thermal expansion is the process where a substance changes its size – length, area, or volume – when its temperature changes. Most materials expand when heated and contract when cooled. This happens because heating increases the kinetic energy of the particles, making them vibrate more vigorously and spread further apart. A good real-world example of this is seen in bridges, which often have expansion joints to allow for changes in length with temperature fluctuations.

**Fitting the iron rim on the wooden wheel:**
1. The diameter of the iron ring is slightly less than that of the wooden wheel.
2. So, it cannot be easily slipped on from the rim of a wooden wheel.
3. The iron ring is, therefore, first heated to a higher temperature so that it expands in size and the hot ring is then easily slipped over to the rim of the wooden wheel.
4. Coldwater is now poured on the iron ring so that it contracts in size and holds the wooden wheel tightly.

**Riveting:**
1. Rivets are used to join two steel plates together.
2. A hot rivet is driven through the hole in the plates.
3. One end of the rivet is hammered to form a new rivet head.
4. When cooled, the rivet will contract and hold the two plates tightly together.

**Cracking of a thick glass tumbler:**
1. Glass is a poor conductor of heat.
2. When hot liquid is poured into the tumbler, the inner surface of the tumbler becomes hot and expands while the outer surface remains at room temperature and does not expand.
3. Due to this unequal expansion, the tumbler cracks.
In simple words: Thermal expansion means things get bigger when they get hot. For example, to put an iron ring on a wooden wheel, we heat the ring so it gets bigger and fits. Then, we cool it, and it shrinks to hold the wheel tightly. This principle is also used in riveting to join metal plates. But sometimes, like with normal glass, uneven expansion can cause things to crack.

🎯 Exam Tip: Define thermal expansion clearly and then illustrate with 2-3 distinct, well-explained examples that demonstrate its applications and consequences. Detail the steps for each example.

X. Questions Based On Higher Order Thinking Skills

 

Question 1. When a window is accidentally left open on a winter night, will you feel uncomfortable because the cold is getting in, or because the heat is escaping from the room?
Answer:
1. When a window is left open on a winter night, I will feel uncomfortable because the heat is escaping from the room.
2. The heat will transfer from the high temperature (inside the room) to the low temperature (outside the room).
During winter, our bodies are warmer than the surrounding air. We lose heat to the colder environment, which makes us feel cold. A good way to think about it is that coldness isn't a substance that moves; it's the absence of heat.
3. During winter, cold air enters the room, so room temperature will decrease.
In simple words: On a cold winter night, you feel uncomfortable because the warmth from inside your room escapes outside through the open window, making the room colder. Heat always moves from warmer places to colder places.

🎯 Exam Tip: Explain that "cold" is not a physical entity that "gets in," but rather the sensation of heat leaving a warmer area to a colder one. This shows a deeper understanding of heat transfer.

 

Question 2. Suppose your normal body temperature was lower than what it is. How would the sensation of hot and cold change?
Answer:
1. If our body temperature was lower than normal, we would feel hot from the surrounding environment more often.
2. This is because the surrounding temperature would often be higher compared to our lower body temperature.
When our body temperature is lower, objects that normally feel cool or neutral would now feel warm, because heat would flow from them into our cooler bodies. The perception of hot and cold is always relative to our own body temperature.
In simple words: If our body was normally cooler, then things that usually feel just right or even cool would start to feel hot. This is because our bodies would take in more heat from them.

🎯 Exam Tip: Emphasize that the sensation of hot and cold is relative to our body temperature. A lower body temperature means we would perceive lower external temperatures as warm, as heat flows into us.

 

Question 3. If you heat a circular disk with a hole, what change do you expect in the diameter of the hole? Remember that the effect of heating increases the separation between any pair of particles.
Answer: If a circular disk with a hole is heated, the diameter of the hole will increase. Many people might think the hole would shrink, but this is not correct. When the disk is heated, all parts of it expand, including the material surrounding the hole. Imagine the hole as part of the metal itself; as the metal expands outwards, the empty space within it also expands proportionally. The material itself gets larger, and the empty space inside also grows bigger as if the entire object were simply scaled up.
For example, if you want to insert one hollow pipe inside another hollow pipe of the same diameter, just heat any one and insert the second one into the heated pipe. This explains the answer in an easy way. So it says that diameter will increase with increasing temperature.
In simple words: When you heat a disk with a hole, the hole actually gets bigger, not smaller. Think of the disk growing larger everywhere, including the empty space inside it. The heat makes all the particles spread out, so the hole expands along with the rest of the metal.

🎯 Exam Tip: A common misconception is that the hole shrinks. Remember that thermal expansion acts on all dimensions of an object uniformly, meaning the hole expands as if it were made of the same material.

I. Choose The Right Answer:

 

Question 1. When an electric current is passing through the conductor __________ energy is produced.
(a) Electric
(b) Heat
(c) Chemical
(d) Kinetic energy
Answer: (b) Heat
In simple words: When electricity flows through a wire, it makes the wire get warm. This warmth is heat energy that is created.

🎯 Exam Tip: Recall that electrical resistance in a conductor converts electrical energy into heat, a principle known as Joule heating.

 

Question 2. One day in 1922, the air temperature was measured at 59°C in the shade in Libya
(a) America
(b) Africa
(c) Antarctica
(d) Europe
Answer: (b) Africa
In simple words: Libya is a country in Africa, where one of the highest air temperatures ever was recorded in the shade.

🎯 Exam Tip: This question tests general knowledge related to record temperatures and geography. Knowing that Libya is in Africa is key.

 

Question 3. The temperature of boiling water is
(a) 0° C
(b) 32° C
(c) 100° C
(d) 110° C
Answer: (c) 100°C
In simple words: Water always starts to boil and turn into steam when it reaches a temperature of 100 degrees Celsius.

🎯 Exam Tip: Remember the standard boiling point of water at sea level, which is 100°C (or 212°F, or 373.15 K).

 

Question 4. The temperature determines the direction flow of __________
(a) heat energy
(b) kinetic energy
(c) potential energy
(d) light energy
Answer: (a) heat energy
In simple words: Temperature is what decides which way heat will travel. Heat always goes from hotter places to colder places.

🎯 Exam Tip: This highlights a core principle of thermodynamics: heat always flows from a region of higher temperature to a region of lower temperature.

 

Question 5. When we cool the liquid it will become __________
(a) Gas
(b) Solid
(c) Vapour
(d) None of the options
Answer: (b) Solid
In simple words: When a liquid gets very cold, its particles slow down and lock into place, changing it into a solid form. This is like water turning into ice.

🎯 Exam Tip: Recall the states of matter and phase changes: cooling a liquid causes it to solidify (freeze), while heating it causes it to vaporize (boil).

II. Say True Or False.

 

Question. State whether the following statements are True or False.
1. Heat is measured in Celsius or centigrade.
2. Temperature in the form of energy.
3. The normal temperature of our body is 37°C.
4. Two objects are said to be in thermal contact if they can exchange heat energy.
5. When the vibrations move from one molecule to another molecule heat will flow.
Answer:
1. False
2. False
3. True
4. True
5. True
In simple words: Heat is energy and is measured in Joules, not Celsius. Temperature is a measure of hotness, not a form of energy itself. Our normal body temperature is indeed around 37°C. Things are in thermal contact if heat can move between them. Heat often moves when tiny particles vibrate and pass that motion to their neighbors.

🎯 Exam Tip: Differentiate clearly between heat (energy, measured in Joules) and temperature (degree of hotness, measured in Celsius/Kelvin). Understand that thermal contact means heat can transfer.

III. Match The Following:

 

Question. Match the following terms.

Answer:
1. - iv (Average kinetic energy of molecule: Temperature)
2. - i (Pyrex glass: Borosilicate)
3. - ii (Thermal expansion: Railway Tracks)
4. - v (Heat transfer: 20°C to 10°C)
5. - iii (Kerosene: Burning)
In simple words: The average energy of moving particles is called temperature. Pyrex glass is a type of borosilicate glass. Thermal expansion is seen in railway tracks. Heat moves from a warmer place (20°C) to a cooler place (10°C). Kerosene is known for burning.

🎯 Exam Tip: For matching, identify the core concept or property for each term. For example, temperature relates to average kinetic energy, and heat transfer happens due to a temperature difference.

IV. Analogy

 

Question. Complete the following analogies.
1. Summer : Sag :: Winter : __________
2. Evaporation : 100°C :: Freezing : __________
Answer:
1. contract
2. 0°C
In simple words: Just as things droop or sag in summer heat, they pull tighter or contract in winter cold. Also, water changes to vapor (evaporates) at 100°C, and it changes to ice (freezes) at 0°C.

🎯 Exam Tip: Analogies test understanding of relationships. Here, the first part relates to thermal expansion/contraction effects of seasons, and the second relates to phase change temperatures.

V. Give Reasons For The Following:

 

Question 1. Gaps are left in between rails while laying a railway track.
Answer: Gaps are left between railway tracks because of thermal expansion. During hot summer days, the metal rails absorb heat and expand. If no gaps were left, the expanding rails would push against each other, causing them to bend or buckle. This buckling could lead to train derailments. The small gaps allow the rails to expand safely without deforming.
In simple words: Gaps are put in railway tracks so the metal can expand when it gets hot in summer. Without these gaps, the tracks would bend and become dangerous.

🎯 Exam Tip: The key reason is thermal expansion. Explain that without gaps, the expanding rails would buckle, posing a safety risk.

 

Question 2. Hot metal ball of 80°C is dipped into water of 80°C. The ball will not contract.
Answer: The hot metal ball will not contract when dipped into water of the same temperature (80°C) because there is no temperature difference between them. Contraction (or expansion) occurs when an object loses (or gains) heat due to a temperature gradient. Since both the ball and water are at 80°C, they are in thermal equilibrium, meaning no net heat transfer will occur, and thus no change in the ball's size due to temperature will happen.
In simple words: The metal ball won't shrink because both the ball and the water are at the same temperature. Heat only moves when one thing is hotter than the other, so there's no heat movement to make the ball contract.

🎯 Exam Tip: Explain that contraction is caused by heat loss due to a temperature difference. Since there is no temperature difference, there is no heat transfer, and thus no contraction.

VI. Very Short Answer:

 

Question 1. What are the sources of heat?
Answer: The main natural source of heat is the Sun. Other important sources include combustion (like burning wood or gas), friction (like rubbing your hands together), and electricity (as used in heaters). Many processes, from chemical reactions to nuclear reactions, also generate heat.
In simple words: The sun is the main source of heat. We also get heat from burning things, rubbing things together, and using electricity.

🎯 Exam Tip: List both natural (Sun) and artificial (combustion, friction, electricity) sources of heat to provide a comprehensive answer.

 

Question 2. Define - heat.
Answer: Heat is a form of energy that is transferred from a region of higher temperature to a region of lower temperature. It is related to the total kinetic and potential energy of the atoms and molecules within a substance, causing them to move faster and further apart.
In simple words: Heat is a type of energy that moves from hotter places to colder places. It makes the tiny parts of a thing move faster and spread out.

🎯 Exam Tip: Define heat as "energy in transit" or "energy transferred" due to a temperature difference, and mention its connection to molecular motion.

 

Question 3. How will you identify two objects are said to be in thermal equilibrium?
Answer: Two objects are in thermal equilibrium if they have the same temperature and no net heat flows between them when they are in thermal contact. If you place a thermometer in contact with both objects and it reads the same temperature for both, then they are in thermal equilibrium.
In simple words: You can tell two objects are in thermal equilibrium if they are touching and no heat is moving between them. This also means they both have the same temperature.

🎯 Exam Tip: The key indicators of thermal equilibrium are "same temperature" and "no net heat transfer" between objects in contact.

 

Question 4. What are the measuring unit of temperature?
Answer: The SI unit of temperature is Kelvin (K). Other common units used for measuring temperature include Celsius (°C) and Fahrenheit (°F). Each unit has a different scale, but they all measure the same physical quantity.
In simple words: The standard unit for temperature is Kelvin. We also commonly use Celsius and Fahrenheit to measure how hot or cold something is.

🎯 Exam Tip: Always list the SI unit (Kelvin) first, then mention other commonly used units like Celsius and Fahrenheit.

 

Question 5. What will determine the direction of flow of heat from one object to another?
Answer: The temperature difference between two objects will determine the direction of heat flow. Heat always flows from the object with a higher temperature to the object with a lower temperature. This process continues until both objects reach thermal equilibrium.
In simple words: The temperature difference between two things decides which way heat will move. Heat always goes from the hotter object to the colder one.

🎯 Exam Tip: Clearly state that "temperature difference" is the deciding factor, and specify the direction: from higher to lower temperature.

VII. Long Answer Questions:

 

Question 1. Explain linear expansion with an experiment.
Answer: Linear expansion refers to the increase in the length of a material when its temperature is raised. This phenomenon occurs because the increased thermal energy causes the atoms or molecules within the material to vibrate with greater amplitude and move further apart, resulting in an overall elongation.

**Experiment: Demonstrating Linear Expansion**

**Aim:** To show that solids expand when heated.

**Materials:** A small bulb, a dry cell (battery), a candle, a cycle spoke, a coin, and two small wooden blocks.

**Procedure:**
1. Place one end of the cycle spoke firmly on a wooden block. Connect an electric wire to this end of the spoke and hold it in place with a stone.
2. Place the other end of the cycle spoke such that it is free to expand.
3. Wrap an electric wire around the coin and place it on a separate block, positioned so the free end of the spoke is just barely not touching it.
4. Connect the bulb and the dry cell to the free ends of the wires (one from the spoke, one from the coin) to complete an electrical circuit, but with a small gap where the spoke is supposed to touch the coin.
5. Light the candle and use its flame to gently heat the cycle spoke.

**Observation & Conclusion:**
When the cycle spoke is heated, its length will increase (linear expansion). This expansion will cause the spoke to touch the coin, completing the electrical circuit. As a result, the bulb will glow, indicating that the spoke has expanded. When the spoke is allowed to cool, it will contract, moving away from the coin, breaking the circuit, and causing the bulb to turn off. This experiment clearly demonstrates that solids undergo linear expansion when heated.

In simple words: Linear expansion is when a material gets longer if you heat it. In an experiment, we can heat a metal rod (spoke) with a candle. As it gets hot, it expands and touches a coin, completing a circuit that lights up a bulb. When it cools, it shrinks, and the bulb turns off, showing it got shorter.

🎯 Exam Tip: When describing an experiment, include the aim, materials, clear step-by-step procedure, and precise observations leading to a conclusion, as done here.

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