11.1 Temperature and heat

Temperature and heat are fundamental concepts in mechanics, linking particle motion to energy transfer. They explain how materials behave under different thermal conditions, affecting everything from engine efficiency to structural integrity.

Understanding temperature scales, heat transfer mechanisms, and thermal properties of materials is crucial for engineers. These concepts guide the design of heat engines, thermal management systems, and help predict how mechanical systems will perform in varying thermal environments.

Definition of temperature

• Temperature quantifies the average kinetic energy of particles in a substance, serving as a fundamental concept in thermodynamics and mechanics
• Relates to the internal energy of a system, playing a crucial role in understanding heat transfer and thermal equilibrium in mechanical systems

Molecular kinetic energy

Top images from around the web for Molecular kinetic energy

• 

  Phase Changes | Boundless Chemistry View original

  Is this image relevant?

• 

  Kinetic Molecular Theory of Matter | Boundless Chemistry View original

  Is this image relevant?

• 

  The Kinetic-Molecular Theory | Introductory Chemistry – Lecture & Lab View original

  Is this image relevant?

• 

  Phase Changes | Boundless Chemistry View original

  Is this image relevant?

• 

  Kinetic Molecular Theory of Matter | Boundless Chemistry View original

  Is this image relevant?

1 of 3

Top images from around the web for Molecular kinetic energy

• 

  Phase Changes | Boundless Chemistry View original

  Is this image relevant?

• 

  Kinetic Molecular Theory of Matter | Boundless Chemistry View original

  Is this image relevant?

• 

  The Kinetic-Molecular Theory | Introductory Chemistry – Lecture & Lab View original

  Is this image relevant?

• 

  Phase Changes | Boundless Chemistry View original

  Is this image relevant?

• 

  Kinetic Molecular Theory of Matter | Boundless Chemistry View original

  Is this image relevant?

1 of 3

• Describes the energy associated with the random motion of particles in a substance
• Directly proportional to temperature, increasing as particles move faster
• Affects material properties such as thermal expansion and phase changes
• Measured in joules (J) and calculated using the formula $E_k = \frac{3}{2}kT$, where k is Boltzmann's constant and T is temperature

Temperature scales

• Celsius scale bases 0°C on water's freezing point and 100°C on its boiling point at standard atmospheric pressure
• Fahrenheit scale sets 32°F as water's freezing point and 212°F as its boiling point
• Kelvin scale, used in scientific calculations, starts at absolute zero (-273.15°C)
• Conversion formulas between scales:
  • °F to °C: $°C = (°F - 32) × \frac{5}{9}$
  • K to °C: $°C = K - 273.15$

Heat vs temperature

• Heat represents the total thermal energy transferred between systems, while temperature measures the average kinetic energy of particles
• Understanding this distinction aids in analyzing thermal processes in mechanical systems

Thermal energy transfer

• Occurs when there's a temperature difference between systems or objects
• Measured in joules (J) or calories (cal), with 1 cal = 4.186 J
• Follows the principle of energy conservation, crucial in thermodynamic analyses
• Affects material properties and behavior in mechanical systems

Specific heat capacity

• Defines the amount of heat required to raise the temperature of 1 kg of a substance by 1°C
• Measured in J/(kg·°C) or cal/(g·°C)
• Varies among materials, influencing their thermal behavior and applications in mechanics
• Calculated using the formula $Q = mc\Delta T$, where Q is heat added, m is mass, c is specific heat capacity, and ΔT is temperature change

Thermal expansion

• Describes the tendency of materials to change in size or shape when heated or cooled
• Critical consideration in mechanical design, especially for structures and precision instruments

Linear expansion

• Refers to the increase in length of a material when heated
• Characterized by the coefficient of linear expansion (α)
• Calculated using the formula $\Delta L = \alpha L_0 \Delta T$, where ΔL is change in length, L₀ is initial length, and ΔT is temperature change
• Varies among materials (metals generally expand more than ceramics)

Volumetric expansion

• Describes the increase in volume of a material when heated
• Characterized by the coefficient of volumetric expansion (β)
• Calculated using the formula $\Delta V = \beta V_0 \Delta T$, where ΔV is change in volume, V₀ is initial volume, and ΔT is temperature change
• Approximately three times the linear expansion coefficient for isotropic materials

Heat transfer mechanisms

• Fundamental processes by which thermal energy moves between systems or objects
• Essential for understanding thermal behavior in mechanical systems and designing thermal management solutions

Conduction

• Transfer of heat through direct contact between particles of matter
• Occurs primarily in solids and is described by Fourier's law of heat conduction
• Rate of heat transfer depends on thermal conductivity, cross-sectional area, and temperature gradient
• Calculated using the formula $q = -kA\frac{dT}{dx}$, where q is heat transfer rate, k is thermal conductivity, A is cross-sectional area, and dT/dx is temperature gradient

Convection

• Transfer of heat by the movement of fluids or gases
• Includes natural convection (buoyancy-driven) and forced convection (externally driven)
• Described by Newton's law of cooling: $q = hA(T_s - T_\infty)$, where h is convective heat transfer coefficient, A is surface area, Ts is surface temperature, and T∞ is fluid temperature

Radiation

• Transfer of heat through electromagnetic waves, requiring no medium
• Governed by the Stefan-Boltzmann law: $q = \epsilon \sigma A(T_1^4 - T_2^4)$, where ε is emissivity, σ is Stefan-Boltzmann constant, A is surface area, and T1 and T2 are absolute temperatures of the radiating and receiving surfaces
• Significant at high temperatures or in vacuum environments

Thermodynamics laws

• Fundamental principles governing energy transfer and transformation in physical systems
• Form the basis for understanding thermal processes in mechanical engineering

First law of thermodynamics

• States that energy cannot be created or destroyed, only converted from one form to another
• Expressed mathematically as $\Delta U = Q - W$, where ΔU is change in internal energy, Q is heat added to the system, and W is work done by the system
• Applies to closed systems and forms the basis for energy balance calculations

Second law of thermodynamics

• Introduces the concept of entropy and states that the total entropy of an isolated system always increases over time
• Explains the directionality of natural processes and the impossibility of perfect heat engines
• Expressed in various forms, including the Clausius statement and the Kelvin-Planck statement
• Leads to the definition of thermodynamic efficiency for heat engines and refrigeration cycles

Phase changes

• Transitions between different states of matter (solid, liquid, gas) due to heat addition or removal
• Crucial in understanding material behavior and designing thermal systems

Latent heat

• Energy required to change the phase of a substance without changing its temperature
• Includes latent heat of fusion (solid to liquid) and latent heat of vaporization (liquid to gas)
• Measured in J/kg or cal/g
• Calculated using the formula $Q = mL$, where Q is heat added or removed, m is mass, and L is specific latent heat

Phase diagrams

• Graphical representations of the states of matter as a function of temperature and pressure
• Show phase boundaries, triple point, and critical point
• Used to predict phase changes and understand material behavior under different conditions
• Include features like sublimation (solid to gas) and deposition (gas to solid)

Thermal equilibrium

• State where two or more systems in thermal contact have reached the same temperature
• Fundamental concept in understanding heat transfer and thermal processes in mechanics

Heat flow direction

• Always occurs from higher temperature regions to lower temperature regions
• Driven by temperature gradients and follows the second law of thermodynamics
• Continues until thermal equilibrium is reached
• Influences material behavior and thermal stress development in mechanical systems

Thermal conductivity

• Measures a material's ability to conduct heat
• Expressed in W/(m·K) or W/(m·°C)
• Varies widely among materials (metals generally have high conductivity, insulators have low conductivity)
• Influences heat transfer rates and thermal management in mechanical systems
• Affects material selection for applications requiring specific thermal properties

Temperature measurement

• Essential for monitoring and controlling thermal processes in mechanical systems
• Utilizes various technologies and principles to accurately determine temperature

Thermometers vs thermistors

• Thermometers use thermal expansion of liquids (mercury, alcohol) to measure temperature
• Thermistors are semiconductor devices that change resistance with temperature
• Thermistors offer faster response times and higher sensitivity than traditional thermometers
• Both have specific applications in mechanical systems based on required accuracy and temperature range

Infrared thermography

• Non-contact temperature measurement technique using infrared radiation emitted by objects
• Produces thermal images or heat maps of surfaces
• Useful for detecting hot spots, thermal insulation issues, and mechanical wear in machinery
• Requires understanding of emissivity and environmental factors for accurate measurements

Heat engines

• Devices that convert thermal energy into mechanical work
• Fundamental to many mechanical systems, including internal combustion engines and power plants

Carnot cycle

• Theoretical thermodynamic cycle representing the most efficient heat engine possible
• Consists of two isothermal and two adiabatic processes
• Maximum efficiency given by $\eta_{Carnot} = 1 - \frac{T_C}{T_H}$, where TC is cold reservoir temperature and TH is hot reservoir temperature
• Serves as a benchmark for evaluating real heat engine performance

Efficiency of heat engines

• Ratio of useful work output to heat input
• Always less than 100% due to the second law of thermodynamics
• Calculated using the formula $\eta = \frac{W_{out}}{Q_{in}}$, where Wout is work output and Qin is heat input
• Influenced by factors such as friction, heat losses, and irreversibilities in the system
• Improvements in efficiency drive advancements in engine design and energy conservation

Thermal properties of materials

• Characteristics that determine how materials behave under different temperature conditions
• Critical for material selection and design in mechanical engineering applications

Thermal conductors vs insulators

• Conductors (metals) have high thermal conductivity, allowing rapid heat transfer
• Insulators (ceramics, polymers) have low thermal conductivity, impeding heat flow
• Selection depends on application requirements (heat dissipation vs thermal isolation)
• Composite materials can combine properties for specific thermal management needs

Thermal expansion coefficients

• Measure a material's tendency to change size with temperature changes
• Linear expansion coefficient (α) for one-dimensional change
• Volumetric expansion coefficient (β) for three-dimensional change
• Vary among materials and affect design considerations for thermal stress and fit tolerances
• Important in applications involving temperature fluctuations or precision alignment

Applications in mechanics

• Integration of thermal concepts in mechanical engineering design and analysis
• Crucial for ensuring proper function and longevity of mechanical systems under various thermal conditions

Thermal stress and strain

• Develop due to temperature changes and constrained thermal expansion or contraction
• Can lead to material deformation, fatigue, or failure if not properly managed
• Calculated using the formula $\sigma_{thermal} = E\alpha\Delta T$, where E is Young's modulus, α is thermal expansion coefficient, and ΔT is temperature change
• Considered in design of structures, engines, and precision instruments

Temperature effects on material strength

• Most materials experience changes in mechanical properties with temperature variations
• Generally, increased temperature leads to decreased yield strength and elastic modulus
• Some materials (certain polymers) may exhibit increased ductility at higher temperatures
• Understanding these effects crucial for selecting materials and designing components for specific operating conditions