Definition and Concept
Nature of Heat
Heat: energy transfer due to temperature difference. Not stored in a body but flows from higher to lower temperature. Unit: joule (J) or calorie (cal).
Thermodynamic Perspective
Heat: path function, depends on process not state. Distinct from internal energy, work. Symbol: Q.
Historical Context
Early caloric theory replaced by kinetic theory. Heat understood as molecular motion transfer.
Mechanisms of Heat Transfer
Conduction
Direct molecular collisions transfer kinetic energy. Dominant in solids. Fourier's law governs conduction rate.
Convection
Heat transfer via fluid motion. Natural (buoyancy-driven) or forced (external source). Described by Newton's law of cooling.
Radiation
Electromagnetic wave emission and absorption. Does not require medium. Stefan-Boltzmann law quantifies emission.
Heat in the First Law of Thermodynamics
First Law Statement
ΔU = Q - W, where ΔU is internal energy change, Q is heat added, W is work done by system.
Role of Heat
Heat: energy crossing system boundary due to temperature difference. Source/sink for internal energy changes.
Work vs Heat
Work: ordered energy transfer. Heat: disordered, random energy transfer.
Heat Capacity and Specific Heat
Definitions
Heat capacity (C): heat required to change temperature by 1 K. Specific heat (c): heat per unit mass per degree.
Types
At constant volume (Cv) and constant pressure (Cp). Cp > Cv in gases due to work done at expansion.
Units and Measurement
Units: J/(kg·K) or J/(mol·K). Measured calorimetrically or via calorimeter apparatus.
Enthalpy and Heat
Definition of Enthalpy
H = U + PV, state function. Represents total heat content at constant pressure.
Heat at Constant Pressure
Heat absorbed/released at constant pressure equals enthalpy change: Qp = ΔH.
Applications
Used in chemical reactions, phase changes, engineering calculations.
Calorimetry Techniques
Basic Principle
Measure heat transfer by temperature change in known mass and specific heat medium.
Types of Calorimeters
Bomb calorimeter: constant volume, combustion reactions. Coffee cup calorimeter: constant pressure, solution reactions.
Calculations
Q = mcΔT, accounting for system and surroundings.
Temperature vs Heat
Distinct Concepts
Temperature: measure of average kinetic energy. Heat: energy transferred due to temperature difference.
Thermodynamic Implications
Temperature is an intensive property; heat is extensive. Temperature change may occur without heat transfer (adiabatic processes).
Measurement Methods
Thermometers measure temperature; calorimeters measure heat transfer indirectly.
Heat Flow and Sign Conventions
Heat Flow Direction
Positive Q: heat added to system. Negative Q: heat removed from system.
Sign Convention in Equations
Consistent use critical for first law application. ΔU = Q - W typically used.
Energy Conservation
Heat flow balanced by internal energy changes and work interactions.
Heat and Phase Changes
Latent Heat
Energy absorbed/released without temperature change during phase transitions.
Types of Latent Heat
Fusion (melting/freezing), vaporization (boiling/condensation), sublimation.
Calculations
Q = mL, where L is latent heat per unit mass.
Mathematical Formulas and Calculations
Heat Transfer by Conduction
Q = -kA (dT/dx) Δtwhere,Q = heat transferred (J),k = thermal conductivity (W/m·K),A = cross-sectional area (m²),dT/dx = temperature gradient,Δt = time interval (s)Heat Transfer by Convection
Q = h A (Ts - Tf) Δtwhere,h = convective heat transfer coefficient (W/m²·K),Ts = surface temperature,Tf = fluid temperatureHeat Transfer by Radiation
Rate given by Stefan-Boltzmann law:
Q = ε σ A (T⁴ - T₀⁴) Δtwhere,ε = emissivity,σ = Stefan-Boltzmann constant (5.67×10⁻⁸ W/m²·K⁴),T, T₀ = absolute temperatures (K)Applications of Heat in Thermodynamics
Engine Cycles
Heat input and rejection govern efficiency (Carnot, Otto, Diesel cycles).
Refrigeration and Heat Pumps
Heat transfer reversed by work input for cooling or heating.
Material Processing
Heat treatments control microstructure via controlled heat transfer.
Limitations and Misconceptions
Heat as a Substance
Heat is not a fluid or substance; it is energy transfer only.
Heat vs Temperature Confusion
Heat transfer may occur without temperature change; temperature alone does not quantify heat content.
Equilibrium Considerations
Heat transfer ceases at thermal equilibrium; irreversible processes generate entropy.
References
- Callen, H. B., Thermodynamics and an Introduction to Thermostatistics, Wiley, 1985, pp. 1-480.
- Çengel, Y. A., and Boles, M. A., Thermodynamics: An Engineering Approach, 8th Ed., McGraw-Hill, 2015, pp. 50-400.
- Moran, M. J., Shapiro, H. N., Fundamentals of Engineering Thermodynamics, 7th Ed., Wiley, 2010, pp. 100-450.
- Atkins, P., de Paula, J., Physical Chemistry, 10th Ed., Oxford University Press, 2014, pp. 200-350.
- Çengel, Y. A., Heat and Mass Transfer: A Practical Approach, 5th Ed., McGraw-Hill, 2007, pp. 60-500.