Internal energy and energy transfers

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レッスンノート

Internal Energy

Internal energy is the total energy stored inside a system by the particles that make up the system due to their motion and positions.
The molecules within a substance have energy in their kinetic store (due to their random motion / vibration) and potential store (due to their position relative to each other).
Together, these stores form the total energy that makes up the internal energy of the system.
Heating a system increases its internal energy.
The temperature of the material is related to the average kinetic energy of the molecules.
The higher the temperature, the higher the kinetic energy of the molecules, and vice versa.
The increase in internal energy from heating can cause the temperature of the system to increase, or produce a change of state (solid to liquid or liquid to gas).

Internal energy of particles in a liquid

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of 1 kg of a substance by 1 °C.
The energy needed to raise the temperature of a given mass by a given amount can be calculated using: ΔE = mcΔθ.
In this equation: ΔE = change in energy (J), m = mass (kg), c = specific heat capacity (J/kg °C), Δθ = change in temperature (°C).
If a substance has a low specific heat capacity, it heats up and cools down quickly because it takes less energy to change its temperature.
If a substance has a high specific heat capacity, it heats up and cools down slowly because it takes more energy to change its temperature.
Specific heat capacity is mainly used for liquids and solids.
The specific heat capacity of different substances determines how useful they would be for a specific purpose, e.g. choosing the best material for kitchen appliances.
Good electrical conductors, such as copper and lead, are excellent conductors of heat due to their low specific heat capacity.
Water has a very high specific heat capacity, making it ideal for heating homes as the water remains hot in a radiator for a long time.

Diagram of apparatus for investigating specific heat capacity

Latent Heat

The energy needed for a substance to change state is called latent heat.
When a change of state occurs, the energy transferred to or away from a substance changes the internal energy of the substance but not its temperature.
Whilst the substance is changing state (e.g. from liquid to gas), the temperature of the substance remains constant, despite the fact that energy is still being transferred to the substance.
This is because the energy is being used to overcome intermolecular forces of attraction between the molecules instead of increasing the kinetic energy of the molecules (and hence the temperature).
Molecules in a solid are tightly bound together, whereas, in a liquid, they are free to flow over one another.
To change the state from solid to a liquid, the molecules need to gain enough energy to overcome intermolecular forces of attraction holding them in their rigid solid structure.
Molecules in a liquid are less tightly bound together, whereas, in a gas, they are free to move completely apart from one another.
To change the state from a liquid to a gas, the molecules need to gain enough energy to overcome the intermolecular forces of attraction holding them close together in their liquid structure.

Specific Latent Heat

Specific latent heat is defined as the amount of energy required to change the state of 1 kg of a substance with no change in temperature.
There are two types of specific latent heat: specific latent heat of fusion (solid to liquid, or liquid to solid) and specific latent heat of vaporisation (liquid to gas, or gas to liquid).
Latent heat is represented by the symbol L with units joules per kilogram (J/kg).
The amount of energy E required to melt or vaporise a mass m with latent heat L is: E = mL.
In this equation: E = thermal energy required for a change in state (J), m = mass (kg), L = specific latent heat (J/kg).
The specific latent heat of fusion is the energy required to convert 1 kg of a substance between a solid and a liquid state with no change in temperature.
The specific latent heat of vaporisation is the energy required to convert 1 kg between a liquid and a gaseous state with no change in temperature.
For water: specific latent heat of fusion = 330 kJ/kg; specific latent heat of vaporisation = 2.26 MJ/kg.
Evaporating 1 kg of water requires roughly seven times more energy than melting the same amount of ice to form water.

Heating & Cooling Graphs

Heating and cooling graphs summarise how the temperature of a substance changes when energy is transferred to or away from it, and where changes of state occur.
Heating is when energy is transferred to the system, increasing the internal energy of the molecules.
Cooling is when energy is transferred away from the system (or dissipated to the surroundings), decreasing the internal energy of the molecules.
On a heating curve, the sections where the temperature is constant (plateaus) represent a change of state.
During a plateau, energy is still being transferred, but it is used to overcome intermolecular forces of attraction rather than increasing kinetic energy.
For heating: solid → melting → liquid → boiling → gas.
For cooling: gas → condensing → liquid → freezing → solid.
The temperature remains constant during melting and boiling, despite energy being transferred to the substance.

Specific Heat Capacity vs Specific Latent Heat

Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount; the substance remains in the same state.
Specific latent heat is the amount of heat energy needed to cause a change of state; the substance changes state but stays at the same temperature.
Example of specific heat capacity: a liquid heated from 5 °C to 20 °C.
Example of specific latent heat: a liquid evaporating into a gas.
Do not confuse the two: specific heat capacity involves a temperature change, specific latent heat involves a change of state with no temperature change.

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練習問題

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1.Which of the following best defines the internal energy of a system?
Easy
- AThe total kinetic and potential energy of all the particles in the system
- BThe average kinetic energy of the particles in the system
- CThe energy transferred to the system by heating
- DThe energy required to raise the temperature of 1 kg of the system by 1 °C
2.The temperature of a substance is related to the average kinetic energy of its particles.
Easy
True or false?
3.Which of the following is the correct unit for specific heat capacity?
Easy
- AJ/kg
- BJ/kg °C
- CJ/°C
- DJ
4.Which of the following is the correct unit for specific latent heat?
Easy
- AJ/kg °C
- BJ
- CJ/kg
- DJ/°C
5.Which of the following statements about a heating curve are correct? (Select all that apply)
Medium
- AThe plateaus on the curve represent changes of state.
- BDuring a plateau, the temperature remains constant.
- CThe temperature always increases steadily as energy is added.
- DThe sloped sections represent an increase in kinetic energy of the particles.
- EDuring a plateau, no energy is being transferred to the substance.
6.Which of the following is the correct definition of specific latent heat of fusion?
Medium
- AThe energy required to raise the temperature of 1 kg of a substance by 1 °C
- BThe energy required to change 1 kg of a substance from solid to liquid with no change in temperature
- CThe energy required to change 1 kg of a substance from liquid to gas with no change in temperature
- DThe energy required to change the state of a substance without changing its temperature
7.During a change of state, the temperature of a substance remains constant even though energy is being transferred to it.
Easy
True or false?
8.Match each term with its correct definition.
Medium
- Internal energy
- Specific heat capacity
- Specific latent heat of vaporisation
- The energy required to change 1 kg of a substance from liquid to gas with no change in temperature
- The total energy stored by the particles in a system due to their motion and positions
- The energy required to raise the temperature of 1 kg of a substance by 1 °C

もっと問題

9.Place the following stages of a heating curve in the correct order as energy is supplied to a solid substance until it becomes a gas.
Medium
- Solid heats up (temperature rises)
- Solid melts (temperature constant)
- Liquid heats up (temperature rises)
- Liquid boils (temperature constant)
- Gas heats up (temperature rises)
10.A substance has a specific latent heat of fusion of 330 000 J/kg. How much energy is required to melt 0.5 kg of the substance at its melting point?
Hard
- A165 000 J
- B330 000 J
- C660 000 J
- D165 J
11.Which of the following would cause the internal energy of a system to increase? (Select all that apply)
Medium
- AHeating the system
- BCooling the system
- CDoing work on the system
- DThe system expands and does work on its surroundings
- EThe system is left to stand in a vacuum with no energy transfer
12.A pure solid is heated at a constant rate until it becomes a gas. Which of the following statements are correct? (Select all that apply)
Medium
- AThe temperature stays constant while the solid is melting.
- BThe temperature stays constant while the liquid is boiling.
- CThe average kinetic energy of the particles increases during melting.
- DThe potential energy of the particles increases during boiling.
- EEnergy is not transferred to the substance during a change of state.
13.Which of the following are units of specific latent heat? (Select all that apply)
Medium
- AJ/kg
- BJ/kg °C
- CJ
- DJ/g
- EJ/°C
14.Which of the following best describes the internal energy of a system?
Easy
- AThe total kinetic energy and potential energy of all the particles in the system
- BThe average kinetic energy of the particles in the system
- CThe total kinetic energy of the particles in the system only
- DThe energy transferred to the system by heating only
15.A student heats 0.5 kg of a liquid and its temperature rises by 20 °C. The specific heat capacity of the liquid is 3000 J/kg °C. How much energy is transferred to the liquid?
Medium
- A30 000 J
- B3000 J
- C60 000 J
- D1500 J
16.The specific latent heat of vaporisation of a substance is 2.0 × 10⁶ J/kg. How much energy is needed to vaporise 0.25 kg of the substance at its boiling point?
Medium
- A5.0 × 10⁵ J
- B8.0 × 10⁶ J
- C2.0 × 10⁶ J
- D5.0 × 10⁴ J
17.A substance has a specific heat capacity of 2000 J/kg °C and a specific latent heat of fusion of 3.0 × 10⁵ J/kg. How much energy is needed to raise the temperature of 2 kg of the solid by 10 °C and then melt it at its melting point?
Hard
- A6.4 × 10⁵ J
- B4.0 × 10⁴ J
- C6.0 × 10⁵ J
- D1.0 × 10⁶ J
18.The temperature of a substance remains constant while it is boiling, even though energy is being transferred to it.
Easy
True or false?
19.The specific heat capacity of a substance is the energy required to change the state of 1 kg of the substance without a change in temperature.
Easy
True or false?
20.During a change of state, the potential energy of the particles increases while the kinetic energy remains constant.
Medium
True or false?
21.Match each term with its correct description.
Medium
- Internal energy
- Specific heat capacity
- Specific latent heat of fusion
- Specific latent heat of vaporisation
- The total kinetic and potential energy of all particles in a system
- The energy required to raise the temperature of 1 kg of a substance by 1 °C
- The energy required to change 1 kg of a solid to liquid with no change in temperature
- The energy required to change 1 kg of a liquid to gas with no change in temperature
22.Place the following stages in the correct order as a solid is heated until it becomes a gas.
Medium
- Solid temperature rises
- Solid melts at constant temperature
- Liquid temperature rises
- Liquid boils at constant temperature
- Gas temperature rises
23.What is happening to the substance during the first plateau?
Medium
- AIt is melting; energy is used to overcome intermolecular forces
- BIt is boiling; energy is used to increase kinetic energy
- CIt is melting; energy is used to increase kinetic energy
- DIt is boiling; energy is used to overcome intermolecular forces
24.What is happening to the substance during the second plateau?
Medium
- AIt is boiling; energy is used to overcome intermolecular forces
- BIt is melting; energy is used to increase kinetic energy
- CIt is boiling; energy is used to increase kinetic energy
- DIt is melting; energy is used to overcome intermolecular forces
25.Which of the following statements about a substance during a change of state is correct?
Easy
- AThe temperature remains constant while energy is transferred.
- BThe temperature increases as energy is transferred.
- CThe temperature decreases as energy is transferred.
- DThe temperature remains constant because no energy is transferred.
26.A solid is heated at a constant rate until it melts. Which statement about the energy transferred during melting is correct?
Easy
- AIt increases the kinetic energy of the particles.
- BIt increases the potential energy of the particles.
- CIt is lost to the surroundings.
- DIt decreases the internal energy of the substance.
27.A substance has a specific heat capacity of 900 J/kg °C. How much energy is required to raise the temperature of 0.5 kg of the substance by 10 °C?
Medium
- A4500 J
- B9000 J
- C450 J
- D18000 J
28.The specific latent heat of vaporisation of a substance is 1.5 × 10⁶ J/kg. How much energy is required to vaporise 0.2 kg of the substance at its boiling point?
Medium
- A3.0 × 10⁵ J
- B7.5 × 10⁵ J
- C1.5 × 10⁶ J
- D3.0 × 10⁶ J
29.A student heats 0.2 kg of a solid and its temperature rises by 25 °C. The specific heat capacity of the solid is 800 J/kg °C. Calculate the energy transferred.
Medium
- A4000 J
- B160 J
- C400 J
- D16000 J
30.A substance has a specific heat capacity of 500 J/kg °C and a specific latent heat of fusion of 2.0 × 10⁵ J/kg. How much energy is needed to raise the temperature of 0.5 kg of the solid by 20 °C and then melt it at its melting point?
Medium
- A5.0 × 10³ J
- B1.0 × 10⁵ J
- C1.05 × 10⁵ J
- D1.1 × 10⁵ J
31.A pure solid is heated at a constant rate. The graph of temperature against time shows two plateaus. Which statement about the energy supplied during the plateaus is correct?
Medium
- AEnergy is used to increase the kinetic energy of the particles.
- BEnergy is used to overcome intermolecular forces.
- CNo energy is supplied during the plateaus.
- DEnergy is used to decrease the internal energy of the substance.
32.A substance has a specific heat capacity of 2000 J/kg °C and a specific latent heat of vaporisation of 5.0 × 10⁵ J/kg. How much energy is required to heat 0.1 kg of the liquid from 20 °C to its boiling point at 80 °C and then completely vaporise it?
Hard
- A1.2 × 10⁴ J
- B5.0 × 10⁴ J
- C6.2 × 10⁴ J
- D1.0 × 10⁵ J
33.A cooling curve for a gas is plotted. Which of the following statements about the cooling curve is correct?
Hard
- AThe temperature decreases continuously until the gas becomes a solid.
- BThe temperature remains constant during condensation and freezing.
- CThe temperature increases during condensation.
- DThere are no plateaus on a cooling curve.
34.The specific latent heat of fusion of water is 3.3 × 10⁵ J/kg. How much energy is required to melt 0.2 kg of ice at 0 °C?
Medium
- A6.6 × 10⁴ J
- B1.65 × 10⁵ J
- C3.3 × 10⁵ J
- D6.6 × 10⁵ J
35.A student heats 0.3 kg of a substance. The temperature rises from 20 °C to 70 °C. The energy supplied is 9000 J. Calculate the specific heat capacity of the substance.
Hard
- A600 J/kg °C
- B300 J/kg °C
- C150 J/kg °C
- D1200 J/kg °C
36.Which of the following statements about internal energy are correct? (Select all that apply)
Medium
- AInternal energy is the total kinetic and potential energy of the particles in a system.
- BHeating a system always increases its temperature.
- CDuring a change of state, the internal energy of the system remains constant.
- DThe internal energy of a gas increases when it is heated.
- EInternal energy is the same as temperature.
37.The temperature of a substance increases while it is melting.
Easy
True or false?
38.Specific latent heat is the energy required to change the state of 1 kg of a substance without a change in temperature.
Medium
True or false?
39.Which statement about the energy supplied during the plateaus is correct?
Hard
- AIt increases the kinetic energy of the particles.
- BIt increases the potential energy of the particles.
- CIt is not supplied during the plateaus.
- DIt decreases the internal energy of the substance.
40.A student supplies 12 000 J of energy to an aluminium block with an electric heater and uses the temperature rise to calculate the specific heat capacity. The value obtained is higher than the accepted value for aluminium (910 J/kg °C). Which of the following is the most likely reason for this?
Hard
- AEnergy is transferred to the surroundings, so the calculated value is too high.
- BThe thermometer has a zero error, making the temperature change too large.
- CThe heater transfers energy to the surroundings, so the actual energy absorbed by the block is less than 12 000 J.
- DThe mass of the block was measured incorrectly.
41.Complete the definitions by filling in the blanks.
Medium
The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1 ____ of the substance by 1 ____.
42.Calculate the energy required to raise the temperature of 2 kg of water by 10 °C. The specific heat capacity of water is 4200 J/kg °C. Give your answer in joules.
Medium
43.Calculate the energy required to raise the temperature of 3 kg of a substance by 15 °C. The specific heat capacity of the substance is 500 J/kg °C. Give your answer in joules.
Medium
44.Calculate the energy required to melt 0.8 kg of a solid at its melting point. The specific latent heat of fusion is 150 000 J/kg. Give your answer in joules.
Medium
45.Complete the sentence about specific heat capacity.
Medium
The specific heat capacity of a substance is the energy required to raise the temperature of 1 kg of the substance by ____ °C.
46.Complete the equation for a change of state.
Medium
energy for a change of state = mass × ____
47.What is the name of the energy required to change the state of 1 kg of a substance with no change in temperature?
Easy
48.Calculate the energy required to melt 0.8 kg of a solid at its melting point. The specific latent heat of fusion is 150000 J/kg. Give your answer in joules.
Medium
49.Calculate the energy required to raise the temperature of 0.4 kg of aluminium by 15 °C. The specific heat capacity of aluminium is 910 J/kg °C. Give your answer in joules.
Medium
50.A 2.5 kg block of copper is heated and its temperature rises by 8 °C. The specific heat capacity of copper is 390 J/kg °C. Calculate the energy transferred to the copper. Give your answer in joules.
Medium
51.Calculate the energy needed to melt 0.75 kg of ice at 0 °C. The specific latent heat of fusion of water is 3.3 × 10⁵ J/kg. Give your answer in joules.
Medium
52.How much energy is required to vaporise 0.3 kg of water at 100 °C? The specific latent heat of vaporisation of water is 2.26 × 10⁶ J/kg. Give your answer in joules.
Medium
53.Explain why the temperature of a substance remains constant while it is melting, even though energy is being transferred to it.
Hard
54.A student heats a solid until it becomes a gas. Describe what happens to the energy supplied during the two plateaus on the heating curve.
Medium
55.Describe a method the student could use to determine the specific heat capacity of the aluminium block, including the measurements taken and how the result is calculated.
Hard
56.Calculate the energy required to raise the temperature of 2 kg of water by 10 °C. The specific heat capacity of water is 4200 J/kg °C. Give your answer in joules.
Medium
- A84000 J
- B75600 J
- C100800 J
- D92400 J
57.Calculate the energy required to raise the temperature of 3 kg of a substance by 15 °C. The specific heat capacity of the substance is 500 J/kg °C. Give your answer in joules.
Medium
- A22500 J
- B24750 J
- C20250 J
- D27000 J
58.Calculate the energy required to melt 0.8 kg of a solid at its melting point. The specific latent heat of fusion is 150 000 J/kg. Give your answer in joules.
Medium
- A132000 J
- B108000 J
- C120000 J
- D144000 J
59.Calculate the energy required to melt 0.8 kg of a solid at its melting point. The specific latent heat of fusion is 150000 J/kg. Give your answer in joules.
Medium
- A144000 J
- B132000 J
- C120000 J
- D108000 J
60.Calculate the energy required to raise the temperature of 0.4 kg of aluminium by 15 °C. The specific heat capacity of aluminium is 910 J/kg °C. Give your answer in joules.
Medium
- A6006 J
- B6552 J
- C4914 J
- D5460 J
61.A 2.5 kg block of copper is heated and its temperature rises by 8 °C. The specific heat capacity of copper is 390 J/kg °C. Calculate the energy transferred to the copper. Give your answer in joules.
Medium
- A7020 J
- B9360 J
- C8580 J
- D7800 J
62.Calculate the energy needed to melt 0.75 kg of ice at 0 °C. The specific latent heat of fusion of water is 3.3 × 10⁵ J/kg. Give your answer in joules.
Medium
- A222750 J
- B297000 J
- C272250 J
- D247500 J
63.How much energy is required to vaporise 0.3 kg of water at 100 °C? The specific latent heat of vaporisation of water is 2.26 × 10⁶ J/kg. Give your answer in joules.
Medium
- A745800 J
- B678000 J
- C813600 J
- D610200 J

フラッシュカード

What is internal energy?

The total energy stored inside a system by the particles that make up the system due to their motion and positions.

What two energy stores make up the internal energy of a substance?

The kinetic energy store (due to random motion/vibration of particles) and the potential energy store (due to their positions relative to each other).

What happens to the internal energy of a system when it is heated?

Heating increases the internal energy of the system.

What is the relationship between temperature and the average kinetic energy of particles?

The higher the temperature, the higher the average kinetic energy of the particles, and vice versa.

What two things can happen when the internal energy of a system is increased by heating?

The temperature of the system can increase, or a change of state can occur (e.g., solid to liquid or liquid to gas).

Why does the temperature remain constant during a change of state?

Because the energy transferred is used to overcome the intermolecular forces of attraction between particles, increasing their potential energy, while the kinetic energy (and hence temperature) stays the same.

What is specific heat capacity?

The amount of energy required to raise the temperature of 1 kg of a substance by 1 °C.

What equation relates energy transferred, mass, specific heat capacity, and temperature change?

ΔE = mcΔθ, where ΔE is energy transferred (J), m is mass (kg), c is specific heat capacity (J/kg°C), and Δθ is temperature change (°C).

What does a low specific heat capacity mean for how a substance heats up and cools down?

A substance with low specific heat capacity heats up and cools down quickly because it takes less energy to change its temperature.

What does a high specific heat capacity mean for how a substance heats up and cools down?

A substance with high specific heat capacity heats up and cools down slowly because it takes more energy to change its temperature.

Why is water used in radiators for heating homes?

Water has a very high specific heat capacity, so it remains hot for a long time in a radiator.

What is latent heat?

The energy needed for a substance to change state.

What is specific latent heat?

The amount of energy required to change the state of 1 kg of a substance with no change in temperature.

What is the specific latent heat of fusion?

The energy required to convert 1 kg of a substance between solid and liquid states with no change in temperature.

What is the specific latent heat of vaporisation?

The energy required to convert 1 kg of a substance between liquid and gas states with no change in temperature.

What equation relates energy, mass, and specific latent heat?

E = mL, where E is energy (J), m is mass (kg), and L is specific latent heat (J/kg).

On a heating curve, what does a plateau (flat section) represent?

A change of state, where energy is being used to overcome intermolecular forces, so the temperature remains constant.

During melting, what happens to the energy supplied?

The energy is used to overcome the intermolecular forces of attraction holding the particles in their solid structure, so the temperature stays constant.

During boiling, what happens to the energy supplied?

The energy is used to overcome the intermolecular forces of attraction holding the particles in their liquid structure, so the temperature stays constant.

What is the difference between specific heat capacity and specific latent heat?

Specific heat capacity is the energy needed to change the temperature of 1 kg of a substance by 1 °C (no change of state). Specific latent heat is the energy needed to change the state of 1 kg of a substance with no change in temperature.

Why does the temperature of a substance stay constant during melting, even though it is being heated?

Because the energy is used to increase the potential energy of the particles (to overcome intermolecular forces) rather than their kinetic energy.

What happens to the kinetic energy of particles during a change of state?

The kinetic energy remains the same, so the temperature remains constant.

What happens to the potential energy of particles during a change of state?

The potential energy increases as the particles overcome the intermolecular forces of attraction.

In the equation ΔE = mcΔθ, what does each symbol represent and what are their units?

ΔE = change in energy (J), m = mass (kg), c = specific heat capacity (J/kg°C), Δθ = change in temperature (°C).

In the equation E = mL, what does each symbol represent and what are their units?

E = energy (J), m = mass (kg), L = specific latent heat (J/kg).

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