Heat Transfer: Basic Concepts

What are Heat and Temperature?

Heat is a form of energy transferred from one system to another due to a temperature difference. Heat is measured in joules (J) or calories (cal).

Temperature, on the other hand, is a measure of the average kinetic energy of the molecules in a substance. Temperature is measured with a thermometer and is expressed in Celsius (°C), Kelvin (K), or Fahrenheit (°F).

Example: When a cold drink is left at room temperature, it warms up over time. This happens because the temperature of the drink is lower than the ambient temperature, and energy (heat) is transferred from the surrounding air to the drink.

What is Heat Transfer?

Heat transfer is the process of energy moving from a system at higher temperature to a system at lower temperature due to a temperature difference. Heat transfer occurs through three main mechanisms:

• Conduction: The transfer of energy through the vibration of molecules in solids. For example, a metal spoon heats up when placed in hot soup.
• Convection: The transfer of energy through the movement of molecules in fluids (liquids and gases). For instance, warm air from a radiator heats up a room.
• Radiation: The transfer of energy through electromagnetic waves. For example, heat energy from the Sun reaches Earth through radiation.

Example: A hot cup of tea radiates heat into the surrounding air. Heat is transferred from the surface of the cup to the air through conduction and convection, while radiation also causes energy loss.

Laws of Thermodynamics and Heat Transfer

The fundamental laws of thermodynamics provide a framework for understanding heat transfer:

• The First Law of Thermodynamics (Conservation of Energy): Energy cannot be created or destroyed, only transformed from one form to another.
• The Second Law of Thermodynamics: Heat spontaneously flows from high-temperature systems to low-temperature systems.
• The Third Law of Thermodynamics: At absolute zero (0 K), the entropy of a system is at its minimum.

Example: A motor converts chemical energy from fuel into mechanical energy, adhering to the first law of thermodynamics as energy is conserved. However, due to the second law, the efficiency of the motor can never be 100%, as some energy is lost as heat.

Relationship Between Thermodynamics and Heat Transfer

Thermodynamics concerns the conservation of energy, equilibrium states, and transitions between states. It looks at energy changes between the initial and final states of a system but is not concerned with the rate at which these changes occur.

Heat transfer, on the other hand, focuses on non-equilibrium systems. It studies how energy is transferred and how quickly this transfer happens due to a temperature difference.

Example: A refrigerator continuously transfers heat to keep the food inside at low temperatures. Thermodynamics would calculate the energy consumption of the fridge, while heat transfer studies how quickly the fridge cools the items inside.

Types of Energy and Internal Energy

Energy can exist in various forms:

• Thermal Energy: Associated with the kinetic energy of molecules.
• Mechanical Energy: Energy derived from motion or position.
• Chemical Energy: Energy stored in the chemical bonds of molecules.
• Nuclear Energy: Energy related to the bonds within atomic nuclei.
• Internal Energy (U): The total kinetic and potential energy of a system’s molecules. Internal energy is directly related to temperature and phase changes.
• Sensible Energy: Related to the kinetic energy of molecules and observed in temperature changes.
• Latent Energy: Energy absorbed or released during phase changes. For example, latent heat is released when water evaporates.

Example: During the melting of ice, the temperature remains constant (0°C), but latent heat is absorbed, allowing the ice to turn into liquid.

What is Enthalpy?

Enthalpy (H) is the total internal energy of a system, including the product of pressure and volume. It is particularly useful in processes occurring at constant pressure, and it is expressed as:

h = u + Pv

Where:

• u is the internal energy
• P is pressure
• v is volume

Enthalpy is used to analyze energy changes in chemical reactions and phase changes. For example, enthalpy increases during the evaporation of water.

Example: During the boiling of water, the heat energy supplied to the water is expressed as a change in enthalpy. In this process, while the temperature remains constant, the enthalpy increases.

System and Surroundings

In thermodynamics, the universe is divided into two parts for analysis: the system and its surroundings.

System:

A system is the specific portion of the universe chosen for study. It can be a defined amount of matter or a particular region where observations are made. For example, during a chemical reaction, the substances that react and form products inside a reaction vessel represent the system.

Surroundings:

The surroundings consist of everything outside the system. This includes all matter and energy that are not part of the system but can interact with it. For instance, in a laboratory experiment, the air, the container that holds the reaction vessel, and the room itself make up the surroundings.

Types of Systems:

1. Open System:
   An open system exchanges both energy and matter with its surroundings. A typical example is a beaker of water placed in an open area: water may evaporate (matter exchange) while the temperature adjusts through heat exchange with the air.
2. Closed System:
   A closed system can exchange energy with its surroundings but not matter. For example, a sealed container of gas can transfer heat with the external environment while retaining all the gas within it.
3. Isolated System:
   An isolated system does not exchange either energy or matter with its surroundings. A perfectly insulated thermos is an ideal example, as it prevents any heat transfer or material exchange with the outside environment.

Ideal Gas Concept and Properties

Ideal Gas Definition:
An ideal gas is defined as a gas that satisfies the equation

Pv=RT or P=ρRT

where:

• P is the absolute pressure ( Pa or kPa),
• v is the specific volume (m³/kg),
• T is the thermodynamic (absolute) temperature (in K),
• ρ is the specific mass (kg/m³),
• R is the gas constant (kJ/kg·K).

Ideal Gas Behavior:

At low pressures and high temperatures, the specific mass of gases decreases, and they behave like an ideal gas. In this state, the specific heats of the gases depend solely on temperature.

What Is Specific Heat?

Definition:
Specific heat is defined as the energy required to raise the temperature of a unit mass of a substance by one degree.

Types of Specific Heat:

• Specific Heat at Constant Volume (C_v):
  The energy required to raise the temperature of a unit mass of a substance by one degree when the volume is held constant.
• Specific Heat at Constant Pressure (C_p​):
  The energy required to raise the temperature of a unit mass of a substance by one degree when the pressure is held constant.

Relationship Between C_p​ and C_v :

For ideal gases, the specific heat at constant pressure (C_p​) is greater than that at constant volume (C_v). This is because additional energy is required for the gas to expand under constant pressure. For ideal gases, the relationship between these two specific heats is typically given by:

Units of Specific Heat

Specific heat is generally expressed in units such as J/(kg·K) or kJ/(kg·K). These units indicate the amount of energy required to raise the temperature of one kilogram of a substance by one degree (Celsius or Kelvin).

Internal Energy and Enthalpy of Ideal Gases

Internal Energy (u) and Enthalpy (h) Change:

The internal energy and enthalpy of ideal gases can be expressed in terms of their specific heats.

Finite Changes:

Changes in internal energy and enthalpy can be approximately calculated using the specific heat values at the average temperature:

For a system with mass m, the total changes in internal energy and enthalpy are:

Incompressible Substances: Solids and Liquids

Definition of Incompressible Substances:

Substances whose specific volume (or density) does not change with temperature and pressure are called incompressible substances. In practice, solids and liquids are considered incompressible because their specific volumes remain essentially constant.

Specific Heats:

For incompressible substances, the specific heat at constant volume (C_v​) and the specific heat at constant pressure (C_p​) are equal. Therefore, the specific heat for these substances is denoted by a single symbol (C).

Change in Internal Energy:

The change in internal energy of solids and liquids is given by:

Where:

• m: Mass of the system (kg)
• C_ave: Specific heat capacity calculated at the average temperature (kJ/kg·K)
• ΔT: Temperature change (°C or K)

Real Gases and Ideal Gas Approximation

Behavior of Real Gases:

At low pressures, real gases behave similarly to ideal gases, with their specific heat capacities depending solely on temperature.

High Pressure and Low Temperature Conditions:

Under high pressure and low temperature conditions, real gases deviate from ideal gas behavior. In these scenarios, their specific heat capacities become functions of both temperature and pressure.

Energy Transfer and Heat Conduction

Energy Transfer Mechanisms

Energy can be transferred to or from a mass through two fundamental mechanisms: heat (Q) and work (W). If energy transfer results from a temperature difference, it is termed heat transfer. In the absence of a temperature difference, energy transfer is considered work.

Work and Power

• Work (W): Energy transfer across the boundaries of a system. Examples include a rising piston, a rotating shaft, or an electric cable.
• Power: The rate at which work is performed, denoted by W. Power units can be Watts (W) or horsepower (hp) (1 hp = 746 W).

Examples:

• Work-Producing Systems: Automobile engines, hydraulic systems, steam and gas turbines.
• Work-Consuming Systems: Compressors, pumps, and mixers.

A system’s energy decreases when performing work and increases when work is done on it.

Heat Transfer and Thermal Energy

In everyday language, “heat” often refers to sensible and latent forms of internal energy. However, in thermodynamics, these energy forms are collectively termed thermal (heat) energy.

Heat Terms and Usage

• Heat Flow: Transfer of thermal energy.
• Heat Addition/Removal: Transfer of heat into or out of a system.
• Heat Absorption/Gain/Loss: Absorption or loss of thermal energy.
• Heat Reservoir: A system that stores thermal energy.
• Electrical Heating: Conversion of electrical energy into heat.
• Latent Heat: Energy transferred during phase changes.
• Body Heat: Thermal energy content of a body.

These terms are commonly used in both everyday language and scientific literature. For instance, “body heat” refers to the thermal energy content of a body.

Heat Transfer Rate and Heat Flux

The heat transfer rate (Q) is the amount of heat transferred per unit time, expressed in Watts (W). When the heat transfer rate is known, the total heat transferred over a specific time interval is calculated as:

If the heat transfer rate is constant, this simplifies to:

Heat Flux

Heat flux (q) is the heat transfer rate per unit area perpendicular to the direction of heat transfer, expressed in W/m². It is calculated as:

Here, A is the heat transfer area. Heat flux can vary with the surface’s position and time.

First Law of Thermodynamics

The First Law of Thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed; it can only be transformed from one form to another. Consequently, even the smallest amount of energy within a system must be considered.The total energy change (increase or decrease) of a system during a process is equal to the difference between the total energies entering and leaving during the process.

Energy can be transferred from a system by the flow of heat, work or mass. The total energy of a simple compressible system consists of internal energy, kinetic energy and potential energy. In this case the energy balance is written as follows:

The change in a system’s total energy equals the difference between the total energy entering and leaving the system.

Mathematically:

This equation accounts for the energy balance of any system, including internal energy, kinetic energy, and potential energy.

Energy Balance Equation

In any process, the energy balance can be written as:

Where:

Energy Balance in Terms of Rate

Energy is a property, and its value remains unchanged unless the state of the system changes. In a steady process, the system’s energy change is zero (ΔE_system = 0 )

In this case, the energy balance is expressed as:

If the system undergoes a continuous process:

Energy Balance for Closed Systems (Constant Mass)

A closed system consists of a constant mass. In practice, for many systems, the total energy (EEE) comprises internal energy (UUU). In closed systems, changes in velocity and elevation are often negligible. Thus, the energy equation simplifies to:

Where:

• m: Mass of the system
• c_v​: Specific heat at constant volume
• ΔT : Temperature change

If there is no work interaction within the system boundaries, the energy balance further simplifies to:

This equation is fundamental for closed systems where only heat transfer occurs.

Surface Energy Balance

The surface energy balance is a fundamental concept in analyzing energy transfers occurring through mechanisms such as conduction, convection, and radiation. Since a surface lacks volume and mass, it inherently possesses no energy. Consequently, surfaces are treated as hypothetical systems with constant energy content during steady-state or continuous flow processes. In this context, the energy balance for a surface is expressed as:

This equation applies to both time-dependent and time-independent scenarios. Due to the absence of volume, the surface energy balance does not account for internal energy generation.