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, with 0 K defined as absolute zero, the lowest possible temperature where particles have minimal motion.

• Absolute zero: −273.15°C or 0 K

• Conversion:

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 vibrate more vigorously and move slightly farther apart as temperature increases.

Worked Example: Length Change Due to Temperature Change

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

Example: Thermal Expansion in Engineering

Gaps are left between segments of railroad tracks to allow for thermal expansion. Without these gaps, tracks could buckle on hot days due to expansion.

Thermal Expansion of Water

Water exhibits anomalous expansion: between 0°C and 4°C, it contracts as temperature increases, reaching maximum density at 4°C. 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:

• 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 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 K. The heat required to change the temperature of a 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 K. 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 heat required for a phase change is:

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

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 values are characteristic of each substance.

Mechanisms of Heat Transfer

Overview of Heat Transfer

Heat can be transferred by three mechanisms: conduction, convection, and radiation.

• Conduction: Transfer of heat through a material without bulk movement of the material.

• Convection: Transfer of heat by the movement of fluids (liquids or gases).

• Radiation: Transfer of heat by electromagnetic waves, which does not require a medium.

Conduction of Heat

In conduction, heat flows from a region of higher temperature to lower temperature. The rate of heat transfer through a rod is:

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

Convection of Heat

Convection involves the bulk movement of fluid, carrying heat from one place to another. It is common in liquids and gases and is responsible for many natural phenomena, such as ocean currents and atmospheric circulation.

Radiation of Heat

Radiation is the transfer of energy by electromagnetic waves. All objects emit radiation depending on their temperature. The Stefan-Boltzmann law gives the power radiated by a surface:

• Where is the emissivity, is the Stefan-Boltzmann constant, is the 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. This greenhouse effect contributes to global warming, as shown by the increase in global average temperatures over time.