Table of Contents
Temperature, Heat and Thermal Equilibrium
1. Introduction
Heat and temperature are fundamental concepts in thermal physics. They are closely related but describe different physical quantities.
Temperature indicates the thermal condition of a body and determines the direction in which heat flows spontaneously. Heat is energy transferred from one body or system to another because of a temperature difference.
Thermal equilibrium occurs when bodies in thermal contact reach the same temperature and there is no net transfer of heat between them.
These concepts form the foundation of thermodynamics, meteorology, engineering, environmental science and everyday thermal applications.
2. Temperature
2.1 Definition of Temperature
Temperature is a physical quantity that indicates the thermal state of a substance and determines the direction of spontaneous heat transfer between bodies in thermal contact.
Heat flows spontaneously from a region of higher temperature to a region of lower temperature until thermal equilibrium is reached.
The SI base unit of temperature is the kelvin (K).
Other commonly used temperature scales include:
- Celsius (°C)
- Fahrenheit (°F)
2.2 Molecular Interpretation of Temperature
Matter consists of atoms and molecules that are in continuous motion.
In a gas, molecules move randomly and possess translational kinetic energy. In liquids and solids, particles also possess kinetic and potential energy associated with their motion and interactions.
For an ideal gas, the average translational kinetic energy of its molecules is directly proportional to absolute temperature.
[
\overline{E_k}=\frac{3}{2}k_BT
]
Where:
- (\overline{E_k}) = average translational kinetic energy per molecule
- (k_B) = Boltzmann constant
- (T) = absolute temperature in kelvin
The Boltzmann constant is approximately:
[
k_B=1.380649\times10^{-23},J/K
]
This relationship applies to the average translational kinetic energy of molecules in a classical ideal gas.
2.3 Temperature and Internal Energy
Temperature and internal energy are not the same.
Internal energy is the total microscopic energy of a system, including the kinetic and potential energies associated with its particles.
Temperature is related to the distribution of microscopic energy among particles.
A large quantity of water at a moderate temperature may possess more total internal energy than a small quantity of water at a higher temperature.
Therefore, temperature alone does not determine the total internal energy of a body.
3. Heat
3.1 Definition of Heat
Heat is energy transferred between systems or bodies because of a temperature difference.
Heat is not a substance stored inside an object. Rather, it is energy in transit across the boundary of a system due to a temperature difference.
The SI unit of heat is the joule (J).
Another traditional unit is the calorie.
[
1,cal\approx4.184,J
]
A kilocalorie (kcal) is equal to 1000 calories.
3.2 Direction of Heat Transfer
Under ordinary conditions, heat flows spontaneously from a hotter body to a colder body.
For example:
- A hot cup of tea cools in a room.
- Ice melts when placed in warm water.
- A metal spoon becomes warm when left in hot soup.
- The human body loses heat to colder surroundings.
Heat transfer continues until thermal equilibrium is reached, assuming the bodies form an isolated combined system.
3.3 Heat and Temperature Difference
The amount of heat transferred is not determined by temperature difference alone.
It also depends on:
- Mass of the substance
- Specific heat capacity
- Change in temperature
- Physical changes occurring in the substance
- Heat losses to the surroundings
For a substance undergoing a temperature change without a change of state:
[
Q=mc\Delta T
]
Where:
- (Q) = heat transferred
- (m) = mass
- (c) = specific heat capacity
- (\Delta T) = temperature change
The detailed study of specific heat capacity and calorimetry is covered in Section 3.4.
4. Difference Between Heat and Temperature
| Heat | Temperature |
|---|---|
| Energy transferred due to temperature difference | Measure of thermal state |
| SI unit is joule (J) | SI unit is kelvin (K) |
| Depends on the quantity of energy transferred | Does not depend on the total quantity of substance in the same way |
| Flows spontaneously from higher to lower temperature | Determines the direction of spontaneous heat transfer |
| Is energy in transit | Is a thermodynamic property of a system |
| Measured indirectly through calorimetry | Measured using a thermometer |
A common examination mistake is to describe heat as the temperature of a body. Heat and temperature are distinct physical concepts.
5. Thermal Equilibrium
5.1 Definition
Thermal equilibrium is the condition in which two or more bodies in thermal contact have the same temperature and there is no net heat transfer between them.
For example, when a cold metal object is placed in warm water, heat flows from the water to the metal until both reach the same temperature, provided no significant heat is exchanged with the surroundings.
5.2 Conditions for Thermal Equilibrium
- The bodies have the same temperature.
- There is no net heat transfer between them.
- Their macroscopic thermal conditions remain stable with time.
- The system has reached a state of thermal balance.
Thermal equilibrium does not necessarily mean that all microscopic molecular motion stops. Molecules continue moving, vibrating and interacting.
5.3 Thermal Contact
Thermal contact means that two systems can exchange energy through heat transfer.
Thermal contact may occur through:
- Direct physical contact
- A conducting material
- A fluid medium
- Thermal radiation across a distance
Two bodies can reach thermal equilibrium even without direct physical contact if they exchange energy through radiation.
6. Zeroth Law of Thermodynamics
6.1 Statement
The Zeroth Law of Thermodynamics states:
If two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.
This law establishes the concept of temperature as a measurable and comparable physical property.
6.2 Explanation
Suppose:
- System A is in thermal equilibrium with system C.
- System B is also in thermal equilibrium with system C.
According to the Zeroth Law, systems A and B are in thermal equilibrium with each other.
This principle forms the scientific basis of thermometry.
6.3 Importance of the Zeroth Law
- Establishes temperature as a meaningful thermodynamic property.
- Provides the basis for comparing temperatures.
- Makes thermometer calibration possible.
- Helps establish thermal equilibrium between systems.
- Supports the practical measurement of temperature in laboratories and industries.
7. Methods of Heat Transfer
Heat can be transferred through three principal mechanisms.
7.1 Conduction
Conduction is the transfer of heat through a substance without the bulk movement of the substance itself.
It occurs mainly through molecular interactions and, in metals, through mobile electrons.
Examples:
- A metal spoon becoming hot in a cup of tea.
- Heat travelling through a metal cooking pan.
- Heat passing through walls and building materials.
Metals are generally good thermal conductors, while materials such as wood, plastic and air are comparatively poor conductors.
7.2 Convection
Convection is the transfer of heat through the bulk movement of a fluid, such as a liquid or gas.
When a fluid is heated, it often expands and becomes less dense. The warmer, less dense fluid rises, while cooler, denser fluid sinks, creating convection currents.
Examples:
- Water circulating while boiling in a pot.
- Warm air rising in a room.
- Atmospheric circulation.
- Sea and land breezes.
Convection may be natural or forced.
Natural convection occurs due to density differences, while forced convection is produced by external devices such as fans and pumps.
7.3 Radiation
Radiation is the transfer of energy through electromagnetic waves.
Unlike conduction and convection, radiation does not require a material medium.
Examples:
- Heat from the Sun reaching the Earth.
- Warmth felt near a fire.
- Infrared radiation emitted by a heated object.
- Thermal imaging cameras detecting emitted radiation.
All objects above absolute zero emit thermal radiation.
7.4 Comparison of Heat Transfer Mechanisms
| Mechanism | Main process | Requires a material medium? | Example |
|---|---|---|---|
| Conduction | Transfer through microscopic interactions | Yes | Heated metal rod |
| Convection | Bulk movement of fluid | Yes, a fluid | Boiling water |
| Radiation | Electromagnetic waves | No | Solar energy reaching Earth |
8. Temperature and the Human Environment
Temperature plays an important role in environmental and biological processes.
- Human body temperature is normally maintained within a relatively narrow range.
- High environmental temperatures increase the risk of heat stress.
- Low temperatures increase heat loss and may cause hypothermia.
- Temperature differences drive atmospheric convection and influence weather.
- Ocean temperatures influence currents and climate systems.
- Industrial processes require controlled temperatures for safety and quality.
9. Worked Examples
Example 1: Converting Calories into Joules
Convert 500 calories into joules.
[
1,cal=4.184,J
]
[
Q=500\times4.184
]
[
Q=2092,J
]
Answer: 2092 J.
Example 2: Temperature Difference
A substance is heated from 20°C to 80°C. Calculate its temperature increase in kelvin.
[
\Delta T=80-20
]
[
\Delta T=60^\circ C
]
A temperature interval of 1°C is equal in magnitude to an interval of 1 K.
Answer: 60 K.
Example 3: Thermal Equilibrium
A warm object at 80°C is placed in contact with a cooler object at 20°C inside an insulated enclosure. In which direction does heat initially flow?
Heat flows from the object at 80°C to the object at 20°C.
The transfer continues until both objects reach the same final temperature.
Answer: From the hotter object to the colder object.
10. Important Examination Distinctions
| Term | Explanation |
|---|---|
| Heat | Energy transferred because of temperature difference |
| Temperature | Measure of the thermal state of a system |
| Internal energy | Microscopic kinetic and potential energy of a system |
| Thermal equilibrium | State with no net heat transfer between bodies in thermal contact |
| Zeroth Law | Establishes the transitive relationship of thermal equilibrium |
| Conduction | Heat transfer without bulk movement of matter |
| Convection | Heat transfer through bulk fluid movement |
| Radiation | Heat transfer through electromagnetic waves |
11. 36 Key Takeaways for Exams
- Temperature indicates the thermal state of a body.
- The SI base unit of temperature is kelvin.
- Heat is energy transferred due to a temperature difference.
- The SI unit of heat is joule.
- One calorie is approximately equal to 4.184 joules.
- Heat flows spontaneously from higher temperature to lower temperature.
- Heat transfer continues until thermal equilibrium is reached in an isolated system.
- Temperature and heat are different physical concepts.
- Temperature does not directly measure the total internal energy of a body.
- Internal energy includes microscopic kinetic and potential energies.
- The average translational kinetic energy of ideal gas molecules is proportional to absolute temperature.
- The Boltzmann constant is approximately (1.380649\times10^{-23},J/K).
- Thermal equilibrium occurs when bodies in thermal contact have the same temperature.
- Thermal equilibrium does not mean molecular motion stops.
- The Zeroth Law of Thermodynamics establishes the basis of temperature measurement.
- If two systems are separately in thermal equilibrium with a third system, they are in equilibrium with each other.
- Thermometers operate on principles associated with thermal equilibrium.
- Heat transfer occurs through conduction, convection and radiation.
- Conduction transfers heat without bulk movement of matter.
- Metals are generally good thermal conductors.
- Wood and plastic are generally poor thermal conductors.
- Convection involves the bulk movement of fluids.
- Natural convection is often caused by temperature-related density differences.
- Forced convection is produced by external devices such as fans and pumps.
- Radiation transfers energy through electromagnetic waves.
- Radiation does not require a material medium.
- Solar energy reaches Earth primarily through radiation.
- All objects above absolute zero emit thermal radiation.
- A metal spoon placed in hot tea becomes warm mainly through conduction.
- Boiling water involves convection currents.
- Warm air generally rises because it is less dense than cooler surrounding air.
- Heat transfer depends on more than temperature difference alone.
- Mass and specific heat capacity influence the heat required to change temperature.
- Heat may be transferred even when bodies are not in direct physical contact.
- Temperature differences drive many atmospheric and oceanic processes.
- Heat, temperature and thermal equilibrium form the foundation of thermodynamics.