3.1 Energy transfer by heat, work, and mass

Energy transfer is the heart of thermodynamics. Heat, work, and mass transfer are the three ways energy moves between systems. Understanding these processes is crucial for grasping how energy flows and changes in various scenarios.

The First Law of Thermodynamics ties it all together. It states that energy can't be created or destroyed, only transferred. This principle helps us analyze and predict energy changes in systems, from simple heat conduction to complex thermodynamic cycles.

Heat, Work, and Mass Transfer

Defining Heat, Work, and Mass Transfer

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• Heat transfers thermal energy between systems or within a system due to a temperature difference
  • Occurs spontaneously from a higher temperature to a lower temperature
• Work transfers energy when a force acts on a system, causing a displacement or change in the system's volume
  • Can be done on a system (positive work) or by a system (negative work)
• Mass transfer moves matter across system boundaries, carrying energy into or out of the system
  • Occurs through processes such as fluid flow (convection) or diffusion
• Key differences between heat, work, and mass transfer:
  • Heat transfer depends on temperature differences
  • Work depends on force and displacement
  • Mass transfer involves the physical movement of matter

Energy Transfer Impact on System Properties

• Conduction transfers heat through direct contact between particles of matter, without any net motion of the matter
  • Occurs due to the collision of particles and the transfer of kinetic energy from more energetic to less energetic particles
  • Examples: heat transfer through a metal rod, heat transfer from a hot pan to a cooler countertop
• Convection transfers heat by the bulk movement of fluids (liquids or gases)
  • Involves the combined effects of conduction and fluid motion
  • Can be natural (driven by buoyancy forces) or forced (driven by external means, such as fans or pumps)
  • Examples: heat transfer in a pot of boiling water, heat transfer in a room with a fan
• Radiation transfers energy through electromagnetic waves or photons, without requiring any medium
  • All objects emit and absorb thermal radiation, depending on their temperature and surface properties
  • Examples: heat transfer from the sun to the Earth, heat transfer from a fire to a person sitting nearby
• Energy transfer mechanisms impact system properties:
  • Heat transfer can lead to changes in temperature
  • Work can result in changes in volume or pressure
  • Mass transfer can affect the composition and total energy of the system

Mechanisms of Energy Transfer

Conduction

• Transfers heat through direct contact between particles of matter, without any net motion of the matter
  • Occurs due to the collision of particles and the transfer of kinetic energy from more energetic to less energetic particles
  • Rate of conduction depends on the temperature gradient, material properties (thermal conductivity), and geometry
  • Examples: heat transfer through a metal spoon in a hot cup of coffee, heat transfer through a wall in a building
• Fourier's law describes the rate of conductive heat transfer:
  • $Q = -kA \frac{dT}{dx}$, where $Q$ is the rate of heat transfer, $k$ is the thermal conductivity, $A$ is the area perpendicular to the direction of heat transfer, and $\frac{dT}{dx}$ is the temperature gradient
• Thermal conductivity ($k$) is a material property that measures the ability of a substance to conduct heat
  • Materials with high thermal conductivity (metals) are good heat conductors
  • Materials with low thermal conductivity (insulators) are poor heat conductors

Convection

• Transfers heat by the bulk movement of fluids (liquids or gases)
  • Involves the combined effects of conduction and fluid motion
  • Can be natural (driven by buoyancy forces) or forced (driven by external means, such as fans or pumps)
  • Examples: heat transfer in a heating system with circulating water, heat transfer in the Earth's atmosphere
• Natural convection occurs when fluid motion is driven by buoyancy forces arising from density differences due to temperature variations
  • Hotter, less dense fluid rises, while cooler, denser fluid sinks
  • Examples: heat transfer in a room without a fan, oceanic currents driven by temperature differences
• Forced convection occurs when fluid motion is driven by external means, such as fans, pumps, or wind
  • Enhances heat transfer by increasing fluid velocity and mixing
  • Examples: heat transfer in a car radiator with a fan, heat transfer in a wind tunnel
• Newton's law of cooling describes convective heat transfer:
  • $Q = hA(T_s - T_\infty)$, where $Q$ is the rate of heat transfer, $h$ is the convective heat transfer coefficient, $A$ is the surface area, $T_s$ is the surface temperature, and $T_\infty$ is the fluid temperature far from the surface

Radiation

• Transfers energy through electromagnetic waves or photons, without requiring any medium
  • All objects emit and absorb thermal radiation, depending on their temperature and surface properties
  • Rate of radiation depends on the surface temperature, surface emissivity, and surface area
  • Examples: heat transfer from the sun to the Earth, heat transfer between a person and their surroundings
• Stefan-Boltzmann law describes the rate of thermal radiation emitted by an object:
  • $Q = \varepsilon \sigma A T^4$, where $Q$ is the rate of heat transfer, $\varepsilon$ is the surface emissivity (a measure of the ability to emit thermal radiation), $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \, W/(m^2 \cdot K^4)$), $A$ is the surface area, and $T$ is the absolute temperature
• Emissivity ($\varepsilon$) is a surface property that measures the ability of a material to emit thermal radiation
  • Ranges from 0 (perfect reflector) to 1 (perfect emitter or blackbody)
  • Examples: polished metals have low emissivity, while rough, dark surfaces have high emissivity

Energy Changes in Thermodynamic Processes

First Law of Thermodynamics and Energy Balance

• States that the change in internal energy of a system ($\Delta U$) equals the heat added to the system ($Q$) minus the work done by the system ($W$)
  • $\Delta U = Q - W$
  • Used to analyze energy changes in thermodynamic processes
• For a closed system (no mass transfer):
  • Heat added to the system and work done on the system are considered positive
  • Heat removed from the system and work done by the system are considered negative
• For an open system (with mass transfer):
  • Change in internal energy includes the energy associated with the mass entering and leaving the system
  • Energy balance equation: $\Delta U = Q - W + \Sigma(m_{in} \times h_{in}) - \Sigma(m_{out} \times h_{out})$, where $m$ represents mass flow rate and $h$ represents specific enthalpy

Thermodynamic Processes and Energy Changes

• Isothermal process: occurs at constant temperature
  • Requires heat transfer to maintain constant temperature while work is done
  • Examples: expansion or compression of an ideal gas in a piston-cylinder device with heat transfer
• Isobaric process: occurs at constant pressure
  • Involves changes in volume and heat transfer
  • Examples: heating or cooling of a gas in a piston-cylinder device with a movable piston
• Isochoric (isovolumetric) process: occurs at constant volume
  • Involves changes in pressure and heat transfer, but no work is done
  • Examples: heating or cooling of a gas in a rigid container
• Adiabatic process: occurs without heat transfer between the system and surroundings
  • Involves changes in temperature, pressure, and volume, with work done by or on the system
  • Examples: rapid compression or expansion of a gas in a piston-cylinder device with insulated walls
• Understanding these processes is crucial for analyzing energy changes in various scenarios
  • Specific equations for each process relate changes in system properties (temperature, pressure, volume) to heat and work
  • Examples: ideal gas law ($PV = nRT$), isentropic process equations ($PV^\gamma = \text{constant}$, where $\gamma$ is the specific heat ratio)

Problem Solving for Heat, Work, and Mass Transfer

Applying Energy Balance Equations

• Use appropriate energy balance equations for closed or open systems
  • Closed systems: $\Delta U = Q - W$
  • Open systems: $\Delta U = Q - W + \Sigma(m_{in} \times h_{in}) - \Sigma(m_{out} \times h_{out})$
• Consider the direction of heat and mass transfer (into or out of the system)
  • Heat added to the system and mass entering the system are positive
  • Heat removed from the system and mass leaving the system are negative
• Use the sign convention for work
  • Work done on the system is positive
  • Work done by the system is negative
• Example: calculating the change in internal energy of a gas in a piston-cylinder device undergoing an isobaric expansion with heat transfer

Using Process-Specific Equations

• Apply specific equations for different thermodynamic processes (isothermal, isobaric, isochoric, adiabatic)
  • Isothermal process: $PV = \text{constant}$, $\Delta U = 0$, $Q = W$
  • Isobaric process: $\Delta H = Q$, $W = P\Delta V$
  • Isochoric process: $\Delta U = Q$, $W = 0$
  • Adiabatic process: $PV^\gamma = \text{constant}$, $Q = 0$, $\Delta U = -W$
• Use these equations to calculate heat, work, or changes in system properties
• Example: calculating the work done by an ideal gas during an isothermal expansion

Applying Specific Heat Capacity and Ideal Gas Law

• Use the concept of specific heat capacity to calculate heat transfer associated with temperature changes
  • $Q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the temperature change
• Apply the ideal gas law ($PV = nRT$) to relate system properties (pressure, volume, temperature, amount of substance)
  • $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the universal gas constant, and $T$ is absolute temperature
• Example: calculating the heat required to raise the temperature of a specific mass of water

Analyzing Thermodynamic Cycle Efficiency

• Calculate the efficiency of thermodynamic cycles (Carnot, Otto, Rankine) using heat, work, and mass transfer concepts
  • Efficiency = (Net work output) / (Heat input)
• Determine the net work output by considering the work done in each stage of the cycle
• Calculate the heat input by analyzing the heat transfer processes in the cycle
• Example: calculating the efficiency of a Carnot cycle operating between two thermal reservoirs at different temperatures