Heat Transfer
1. Thermal Equilibrium and Heat Flow
Learning outcomes
-
I can explain that heat flows naturally from warmer objects to cooler objects.
- I can define thermal equilibrium and describe when it occurs.
- I can predict the direction of heat transfer between two objects.
- I can distinguish between heat transfer and temperature change.
- I can identify examples of thermal equilibrium in everyday life.
Thermal Equilibrium and Heat Flow
Heat Flows from Warmer to Cooler Objects
When two objects at different temperatures interact, thermal energy is transferred from the warmer object to the cooler object.
This transfer of thermal energy is called heat transfer.
For example, if you place a metal spoon into a cup of hot tea:
- the tea is initially warmer than the spoon
- thermal energy transfers from the tea to the spoon
- the spoon becomes warmer
- the tea becomes slightly cooler
The transfer continues until the spoon and tea reach the same temperature.
At that point, they are in thermal equilibrium.
Temperature and Particle Motion
Temperature is related to the average kinetic energy of the particles in a substance.
In a warmer object, particles generally have greater average kinetic energy than particles in a cooler object.
When warmer and cooler materials interact, collisions between particles allow energy to be transferred.
The overall result is:
warmer object → cooler object
The warmer object loses thermal energy while the cooler object gains thermal energy.
This process continues until there is no temperature difference driving a net transfer of thermal energy.
What Is Thermal Equilibrium?
Thermal equilibrium occurs when objects in thermal contact reach the same temperature and there is no net transfer of thermal energy between them.
For example, suppose a block at 80°C is placed in contact with a block at 20°C.
Initially:
80°C object → heat transfer → 20°C object
As energy is transferred:
- the hot object cools
- the cold object warms
- the temperature difference decreases
Eventually, both objects reach the same final temperature.
At this point:
T₁ = T₂
The objects are in thermal equilibrium.
Predicting the Direction of Heat Transfer
The direction of spontaneous heat transfer is determined by temperature, not by the size, mass or total internal energy of the objects.
The basic rule is:
Higher temperature → Lower temperature
For example:
| Object A | Object B | Net heat transfer |
|---|---|---|
| 80°C | 20°C | A → B |
| 10°C | 35°C | B → A |
| 25°C | 25°C | No net transfer |
| −10°C | 5°C | B → A |
Even when both objects are cold, energy still transfers from the object with the higher temperature to the one with the lower temperature.
For example, an ice cube at −15°C placed in a freezer at −5°C will gain thermal energy from its surroundings because −5°C is warmer than −15°C.
Heat and Temperature Are Not the Same Thing
The words heat and temperature are sometimes used as though they mean the same thing, but in physics they describe different concepts.
Temperature
Temperature indicates the thermal state of an object and is related to the average kinetic energy of its particles.
Temperature can be measured in units such as:
- degrees Celsius (°C)
- kelvin (K)
Heat
Heat is thermal energy transferred between systems because of a temperature difference.
Heat is therefore energy in transfer.
Its SI unit is the joule (J).
A useful distinction is:
Temperature tells us how hot or cold something is.
Heat describes energy being transferred because of a temperature difference.
Heat Transfer vs Temperature Change
Heat transfer often causes temperature to change, but the two ideas are not identical.
Consider a cold metal block placed into hot water.
Thermal energy transfers:
hot water → metal block
The block gains energy and its temperature usually rises.
The water loses energy and its temperature usually falls.
However, the amount of heat transferred and the resulting temperature change depend on several factors, including:
- mass
- material
- specific heat capacity
- changes of state
Therefore, the same amount of transferred energy does not necessarily produce the same temperature change in different objects.
Mass Matters
Imagine heating:
- one cup of water
- an entire swimming pool
Raising both by 1°C requires vastly different amounts of energy.
The swimming pool contains much more water and therefore requires much more energy for the same temperature increase.
This demonstrates why temperature alone does not tell us the total thermal energy of an object.
A small cup of boiling water has a higher temperature than a swimming pool at 30°C, but the swimming pool contains vastly more internal energy overall.
Specific Heat Capacity Matters
Different materials require different amounts of energy to change their temperatures.
The relationship can be expressed as:
Q = mcΔT
where:
- Q = energy transferred, in J
- m = mass, in kg
- c = specific heat capacity, in J/(kg·°C)
- ΔT = temperature change, in °C or K
A material with a high specific heat capacity requires more energy to produce a particular temperature change.
Water has a relatively high specific heat capacity, which is one reason it warms and cools more slowly than many other materials.
Worked Example
A 2.0 kg object has a specific heat capacity of 500 J/(kg·°C). Its temperature increases by 10°C.
Calculate the energy transferred to the object.
Use:
Q = mcΔT
Substitute:
Q = 2.0 × 500 × 10
Q = 10,000 J
Therefore:
Q = 10,000 J
The object gained 10 kJ of energy.
Reaching Thermal Equilibrium
Suppose a hot object and a cold object are placed together inside an insulated container.
Initially:
T_hot > T_cold
Energy transfers from the hotter object to the colder object.
As time passes:
- T_hot decreases
- T_cold increases
- the temperature difference becomes smaller
- the rate of net heat transfer generally decreases
Eventually:
T_hot = T_cold
Thermal equilibrium has been reached.
On a temperature-time graph, the temperatures of the two objects move toward the same equilibrium temperature.
Does Energy Transfer Stop Completely?
At thermal equilibrium, we usually say there is no net heat transfer between the objects.
At the microscopic level, particles are still moving, colliding and exchanging energy.
However, because both systems have the same temperature, energy is exchanged in both directions at equal average rates.
Therefore:
energy transfer in one direction = energy transfer in the opposite direction
The net transfer is zero.
This is an important distinction.
Everyday Example: A Hot Drink
Imagine making a cup of hot chocolate.
Initially:
- drink = 80°C
- room = 22°C
Because the drink is warmer:
drink → surroundings
Energy is transferred from the drink to the cup, air, table and other surroundings.
The drink gradually cools.
If left long enough, its temperature approaches the temperature of its surroundings.
The drink and surroundings are then approximately in thermal equilibrium.
Everyday Example: Ice in Water
Suppose an ice cube at 0°C is placed into water at 25°C.
The water is warmer, so:
water → ice
The ice gains thermal energy.
Initially, much of this energy is used to melt the ice rather than raise its temperature.
This illustrates an important idea:
Heat transfer does not always cause an immediate temperature change.
During a change of state, energy can be transferred while temperature remains constant.
Everyday Example: A Thermometer
A thermometer works by reaching thermal equilibrium with the object being measured.
Suppose a thermometer initially at room temperature is placed into warm water.
Thermal energy transfers:
warm water → thermometer
The thermometer warms until its temperature becomes approximately equal to the temperature of the water.
Only then does it provide a reliable measurement.
This explains why a thermometer sometimes needs time before its reading becomes stable.
Everyday Example: Food in a Refrigerator
Suppose warm leftovers are placed in a refrigerator.
The food is initially warmer than the air and other materials inside the refrigerator.
Therefore:
food → refrigerator surroundings
The food loses thermal energy and cools.
Eventually, its temperature approaches the temperature inside the refrigerator.
This is another example of a system moving toward thermal equilibrium.
Methods of Heat Transfer
Thermal energy can be transferred in three major ways.
Conduction
Conduction transfers thermal energy through particle interactions, particularly in solids.
Example:
A metal spoon becomes hot when one end is placed in hot soup.
Convection
Convection transfers thermal energy through the bulk movement of fluids.
Example:
Warm water rises and cooler water sinks in a heated pot.
Thermal Radiation
Thermal radiation transfers energy through electromagnetic waves.
Unlike conduction and convection, radiation does not require matter.
Example:
Energy from the Sun travels through space to Earth.
All three processes can contribute to systems moving toward thermal equilibrium.
Thermal Equilibrium and Insulation
Insulation does not prevent thermal equilibrium forever.
Instead, insulation reduces the rate of energy transfer.
For example, a vacuum flask reduces energy transfer through:
- conduction
- convection
- radiation
As a result, a hot drink remains hot for much longer.
However, given enough time, the drink and its surroundings will still tend toward thermal equilibrium.
This leads to an important distinction:
Insulation slows heat transfer; it does not change the natural direction of heat transfer.
Can Heat Flow from Cold to Hot?
Thermal energy naturally transfers from higher temperature to lower temperature.
However, devices such as refrigerators and air conditioners can move energy from cooler regions to warmer regions.
They can do this only by using an external energy supply.
For example, a refrigerator transfers thermal energy from its cold interior to the warmer room while consuming electrical energy.
This does not contradict the natural direction of spontaneous heat transfer because work is being done on the system.
Thermal Equilibrium and the Zeroth Law
Thermal equilibrium is connected to the Zeroth Law of Thermodynamics.
In simplified form:
If object A is in thermal equilibrium with object C, and object B is also in thermal equilibrium with object C, then A and B are in thermal equilibrium with each other.
Therefore:
If:
T_A = T_C
and:
T_B = T_C
then:
T_A = T_B
This principle makes temperature measurement possible.
A thermometer acts as the third system. Once it reaches thermal equilibrium with an object, its temperature can be used to determine the object's temperature.
Common Mistakes
Mistake: "Cold flows into an object."
In thermal physics, we normally describe thermal energy transferring from the warmer object to the cooler object.
Mistake: "Heat and temperature are the same thing."
Heat is energy transferred because of a temperature difference. Temperature describes the thermal state of a system.
Mistake: "A larger object must have a higher temperature."
Temperature does not depend simply on an object's size.
Mistake: "Thermal equilibrium means particles stop moving."
Particles continue moving. There is simply no net heat transfer between systems at the same temperature.
Mistake: "Insulation stops all heat transfer."
Real insulation reduces the rate of transfer but does not normally eliminate it completely.
Mistake: "If energy is transferred into something, its temperature must rise."
Not necessarily. During a change of state, energy can be transferred without a temperature change.
Key Terms
Thermal energy — energy associated with the microscopic motion and interactions of particles in a system.
Heat transfer — transfer of thermal energy resulting from a temperature difference.
Temperature — a measure related to the average kinetic energy of particles.
Thermal equilibrium — the condition in which systems have the same temperature and there is no net heat transfer between them.
Temperature difference — the difference in temperature between two systems that drives net thermal energy transfer.
Conduction — energy transfer through interactions between particles.
Convection — energy transfer through the movement of a fluid.
Thermal radiation — energy transfer by electromagnetic radiation.
Specific heat capacity — the energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K).
Insulation — material or a system designed to reduce the rate of thermal energy transfer.
Zeroth Law of Thermodynamics — the principle relating thermal equilibrium between multiple systems and providing the basis for temperature measurement.
Key Takeaways
- Thermal energy naturally transfers from higher-temperature objects to lower-temperature objects.
- A temperature difference drives net heat transfer.
- Thermal equilibrium occurs when interacting systems reach the same temperature and there is no net heat transfer.
- Heat and temperature are different concepts.
- Heat describes energy transfer, while temperature describes the thermal state of a system.
- Heat transfer does not always produce a temperature change, particularly during changes of state.
- The temperature change produced by a given energy transfer depends on mass and specific heat capacity.
- Conduction, convection and radiation can all transfer thermal energy.
- Insulation slows heat transfer but does not reverse its natural direction.
- A thermometer measures temperature by approaching thermal equilibrium with the object being measured.
- Refrigerators can transfer energy from cooler to warmer regions because external energy is supplied.
- Thermal equilibrium is fundamental to the Zeroth Law of Thermodynamics.
Check Your Understanding
- In which direction does thermal energy naturally transfer between objects at 70°C and 25°C?
- Define thermal equilibrium.
- Why does a hot drink eventually approach room temperature?
- Explain the difference between heat and temperature.
- Why does a thermometer need time to give an accurate reading?
- Two objects are both at 35°C and are placed in contact. Is there a net heat transfer between them? Explain.
- Why can energy be transferred into melting ice without increasing its temperature?
- Explain why insulation slows the approach to thermal equilibrium but does not prevent it indefinitely.
- A 0.50 kg object with a specific heat capacity of 800 J/(kg·°C) warms by 15°C. Calculate the energy transferred to it.
- Explain how a refrigerator can transfer thermal energy from its cold interior to a warmer room.