Temperature and Heat

Introduction to Temperature and Heat

Temperature and heat are fundamental concepts in thermodynamics, yet they are often confused. Temperature is a measure of the average kinetic energy of the particles in a substance, while heat refers to the energy transferred between objects due to a temperature difference. This chapter focuses on the macroscopic properties of matter, with a microscopic perspective introduced in later chapters.

Temperature and Thermal Equilibrium

Measuring Temperature

Thermometers are devices used to measure temperature. They operate based on physical properties that change with temperature, such as the volume of a liquid in a glass thermometer. When two systems are in thermal equilibrium, they have the same temperature and no net heat flows between them.

Other Types of Thermometers

Modern thermometers, such as temporal artery thermometers, measure infrared radiation emitted from the skin to determine body temperature without direct contact with internal tissues.

The Zeroth Law of Thermodynamics

The Zeroth Law of Thermodynamics states: If system C is in thermal equilibrium with both systems A and B, then A and B are in thermal equilibrium with each other. This law forms the basis for temperature measurement and the use of thermometers.

Temperature Scales

Celsius and Kelvin Scales

The Celsius scale sets 0°C as the freezing point and 100°C as the boiling point of water. The Kelvin scale is the absolute temperature scale, with 0 K as absolute zero, the theoretical temperature at which all molecular motion ceases. The conversion between Celsius and Kelvin is:

• Kelvin to Celsius:

• Celsius to Kelvin:

Thermal Expansion

Linear Thermal Expansion

When the temperature of a solid changes, its length changes proportionally. The change in length is given by:

where is the coefficient of linear expansion, is the original length, and is the temperature change.

Molecular Basis for Thermal Expansion

Thermal expansion can be explained by the increased average distance between atoms as temperature rises. Atoms in a solid are modeled as being connected by springs, and as they vibrate more vigorously with heat, the solid expands.

Length Change Due to Temperature Change: Example

Consider a steel measuring tape calibrated at 20°C. If used at a higher temperature, its length increases, affecting measurement accuracy. Calculations use the linear expansion formula to determine the actual length or measured distance.

Expanding Holes and Volume Expansion

When an object with a hole is heated, both the object and the hole expand. The change in volume is given by:

where is the coefficient of volume expansion ( for isotropic solids), is the original volume, and is the temperature change.

Thermal Expansion in Practice

Thermal expansion is considered in engineering, such as leaving gaps in railroad tracks to prevent buckling on hot days.

Thermal Expansion of Water

Water exhibits anomalous expansion: between 0°C and 4°C, it contracts as temperature increases, making it densest at 4°C. This property causes lakes to freeze from the top down.

Thermal Stress

If a solid is prevented from expanding or contracting as its temperature changes, thermal stress develops. The stress is given by:

where is Young's modulus, is the coefficient of linear expansion, and is the temperature change.

Quantity of Heat

Mechanical Equivalent of Heat

James Joule demonstrated that mechanical work can be converted into heat, establishing the principle of energy conservation. Stirring water with a paddle wheel or direct heating can produce the same temperature increase.

Specific Heat

The specific heat of a substance is the amount of heat required to raise the temperature of 1 kg of the substance by 1°C. The heat required to change the temperature of mass by is:

Molar Heat Capacity

The molar heat capacity is the amount of heat required to raise the temperature of 1 mole of a substance by 1°C. The heat required for moles is:

Phase Changes

Latent Heat and Phase Changes

During a phase change (solid-liquid-gas), the temperature remains constant while heat is absorbed or released. The latent heat is the heat per unit mass required for the phase change:

Heat Added to Ice at a Constant Rate

When heat is added to ice, the temperature rises until it reaches 0°C, then remains constant as the ice melts. After all ice has melted, the temperature of the water rises again.

Heat of Fusion and Vaporization

The heat of fusion is the energy required to melt a solid at its melting point. The heat of vaporization is the energy required to vaporize a liquid at its boiling point. These processes are crucial in everyday phenomena, such as melting metals or evaporation cooling the body.

Mechanisms of Heat Transfer

Conduction

Conduction is the transfer of heat through a material without the movement of the material itself. The rate of heat transfer (heat current) through a rod is:

where is the thermal conductivity, is the cross-sectional area, and are the temperatures at each end, and is the length.

Convection

Convection is the transfer of heat by the movement of fluids (liquids or gases). Heated fluid rises and cooler fluid sinks, creating a circulation pattern that transfers heat.

Radiation

Radiation is the transfer of heat by electromagnetic waves, such as infrared or visible light. All objects emit thermal radiation, and the rate of energy emission is given by the Stefan-Boltzmann law:

where is the emissivity, is the Stefan-Boltzmann constant, is the surface area, and is the absolute temperature.

Radiation and Climate Change

The Earth's surface emits infrared radiation, which is partially absorbed and re-emitted by atmospheric CO2, contributing to the greenhouse effect and global warming. Increased CO2 levels from fossil fuel combustion are linked to rising global temperatures.