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 related to temperature and heat.

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.

• Thermal equilibrium occurs when two systems in contact no longer exchange energy as heat, indicating they are at the same temperature.

Other Types of Thermometers

Modern thermometers, such as temporal artery thermometers, measure infrared radiation emitted by the body to determine 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 underpins the concept of temperature as a measurable and transitive property.

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 SI unit for temperature, starting at absolute zero (0 K), the theoretical point where all molecular motion ceases.

• Absolute zero is −273.15°C.

• To convert Celsius to Kelvin:

Temperature Conversions

Key temperature points and conversions between Celsius and Kelvin are essential for calculations in thermodynamics.

Thermal Expansion

Linear Thermal Expansion

When the temperature of a solid changes, its dimensions change due to the increased average separation between atoms. For moderate temperature changes, 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 understood by modeling atoms as being connected by springs. As temperature increases, the average distance between atoms increases, causing the material to expand in all dimensions.

Length Change Due to Temperature Change – Example

Example problems often involve calculating the new length of a material after a temperature change, using the linear expansion formula.

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.

Thermal Expansion in Engineering

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

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 is crucial for aquatic life in cold climates.

Thermal Stress

If a material 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:

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

Expansion joints in bridges accommodate these changes to prevent structural damage.

Quantity of Heat

Mechanical Equivalent of Heat

James Joule demonstrated that mechanical work can be converted into heat, establishing the principle of energy conservation in thermodynamics.

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 a mass by is:

• Where is the specific heat capacity.

Molar Heat Capacity

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

• Where is the molar heat capacity.

Phase Changes

Latent Heat and Phase Changes

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

• Where is the latent heat of fusion (melting) or vaporization (boiling).

Heat Added to Ice at a Constant Rate

When heat is added to ice, the temperature rises until the melting point is reached, then remains constant during the phase change, and rises again once all ice has melted.

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 concepts explain phenomena such as why people feel cold when wet due to evaporation.

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 through a rod is given by:

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

Convection

Convection is the transfer of heat by the movement of fluids (liquids or gases). It occurs naturally due to differences in density caused by temperature gradients.

Radiation

Radiation is the transfer of energy by electromagnetic waves. All objects emit thermal radiation, and the rate of emission is given by the Stefan-Boltzmann law:

• Where is the Stefan-Boltzmann constant, is the area, is the emissivity, 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.

Additional info: Tables referenced in the text (coefficients of expansion, specific heats, etc.) are not included here but are essential for quantitative problem solving in this chapter.