Temperature and Heat

Introduction

Temperature and heat are fundamental concepts in thermodynamics, often confused in everyday language but distinct in physics. Temperature is a measure of the average kinetic energy of particles in a substance, while heat refers to energy transfer due to temperature differences. This chapter focuses on macroscopic properties and their physical implications.

Temperature and Thermal Equilibrium

A thermometer measures temperature by exploiting the physical property of materials that change with temperature, such as the volume of a liquid. Thermal equilibrium occurs when two systems have the same temperature and no net heat flows between them.

• Thermal equilibrium: Two systems are in thermal equilibrium if they have the same temperature.

• Thermometer operation: The expansion of liquid in a thermometer is used to measure temperature.

Other Types of Thermometers

Modern thermometers include devices that measure infrared radiation, such as temporal artery thermometers. These detect the heat emitted from the skin, providing a non-contact method of temperature measurement.

The Zeroth Law of Thermodynamics

The Zeroth Law of Thermodynamics establishes the concept of temperature. If system C is in thermal equilibrium with both A and B, then A and B are in thermal equilibrium with each other. This law allows the definition of temperature as a measurable property.

• Transitive property: Thermal equilibrium is transitive among systems.

Temperature Scales

Celsius and Kelvin Scales

The Celsius scale is based on the freezing and boiling points of water. The Kelvin scale is the absolute temperature scale, with zero Kelvin representing absolute zero, the point at which the pressure of an ideal gas would be zero.

• Celsius scale: 0°C = freezing point of water, 100°C = boiling point.

• Kelvin scale: 0 K = absolute zero; conversion:

Thermal Expansion

Linear Thermal Expansion

When the temperature of a solid changes, its dimensions change. For moderate temperature changes, the change in length is given by:

• Formula:

• Coefficient of linear expansion (\alpha): Material-specific constant.

Molecular Basis for Thermal Expansion

Atoms in solids are held together by interatomic forces, often modeled as springs. As temperature increases, the average distance between atoms increases, causing expansion in all dimensions.

Length Change Due to Temperature Change – Example

Practical problems often involve calculating the change in length of objects due to temperature variations, such as a steel measuring tape used at different temperatures.

• Example: A steel tape calibrated at 20°C is used at 35°C. The actual length and measured distance must be corrected for thermal expansion.

Expanding Holes and Volume Expansion

When an object with a hole is heated, the hole expands as if it were filled with the material. The change in volume is given by:

• Formula: where

Example of Thermal Expansion

Thermal expansion is considered in engineering, such as gaps in railroad tracks to prevent buckling during hot weather.

Thermal Expansion of Water

Water exhibits anomalous behavior between 0°C and 4°C, where it decreases in volume as temperature increases. This property explains why lakes freeze from the top down.

Thermal Stress

If an object is prevented from expanding or contracting as its temperature changes, thermal stress develops. The force per unit area required to keep the length constant is:

• Formula:

• Expansion joints: Used in bridges to accommodate thermal expansion.

Quantity of Heat

Heat and Work

Heat can be transferred to a substance by doing work (mechanical stirring) or by direct heating. The calorie is defined as the amount of heat required to raise 1 gram of water by 1°C.

Specific Heat

The specific heat of a material is the amount of heat required to raise the temperature of 1 kg of the material by 1 K. The heat required for a mass and temperature change is:

• Formula:

• Specific heat of water: Approximately 4186 J/kg·K

Molar Heat Capacity

The molar heat capacity is the heat required to raise the temperature of one mole of a substance by one kelvin. The heat required for moles and temperature change is:

• Formula:

Phase Changes

Phase Changes and Latent Heat

Substances exist in solid, liquid, and gas phases. During a phase change, temperature remains constant while heat is transferred. Latent heat is the heat per unit mass required for a phase change.

• Formula:

• Heat of fusion: Melting of solids (e.g., gallium).

• Heat of vaporization: Evaporation of liquids (e.g., water from skin).

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) is:

• Formula:

• Thermal conductivity (k): Material property affecting heat flow.

Convection

Convection is the transfer of heat by the movement of fluid masses. It occurs in liquids and gases, where heated regions move and carry energy.

Radiation

Radiation is the transfer of heat by electromagnetic waves, such as infrared or visible light. The Stefan-Boltzmann law describes the heat current due to radiation:

• Formula:

• Emissivity (\epsilon): Surface property; is the Stefan-Boltzmann constant.

Radiation and Climate Change

The Earth's surface emits infrared radiation, which is absorbed and re-emitted by atmospheric CO2, contributing to global warming. Increased CO2 levels are linked to rising global temperatures.

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