♨️Thermodynamics of Fluids Unit 1 – Intro to Fluid Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, and energy in systems
• Fluids include both liquids and gases that continuously deform under shear stress
• Density $(\rho)$ is mass per unit volume, a measure of fluid compactness
• Pressure $(P)$ is force per unit area, resulting from molecular collisions within the fluid
• Temperature $(T)$ quantifies the average kinetic energy of particles in a substance
• Viscosity $(\mu)$ measures a fluid's resistance to flow or internal friction
• Compressibility is the ability of a fluid to change volume under pressure (gases are highly compressible, liquids are nearly incompressible)
• Ideal gas assumes molecules have negligible volume and no intermolecular forces

Fundamental Laws and Principles

• First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • Expressed as $\Delta U = Q - W$, where $\Delta U$ is change in internal energy, $Q$ is heat added, and $W$ is work done by the system
• Second Law of Thermodynamics asserts that entropy (disorder) of an isolated system always increases over time
  • Implies that heat flows naturally from high to low temperature and work is required to transfer heat from low to high temperature
• Zeroth Law of Thermodynamics defines thermal equilibrium: if two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other
• Ideal Gas Law relates pressure, volume, temperature, and amount of gas: $PV = nRT$
  • $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is universal gas constant, and $T$ is absolute temperature
• Dalton's Law states that in a mixture of non-reacting gases, the total pressure equals the sum of the partial pressures of the individual gases

Properties of Fluids

• Fluids are characterized by their ability to flow and take the shape of their container
• Density of a fluid depends on its composition, pressure, and temperature
  • Liquids are generally more dense than gases due to stronger intermolecular forces
• Viscosity arises from intermolecular forces and quantifies a fluid's resistance to deformation
  • Newtonian fluids (water, air) have constant viscosity, while non-Newtonian fluids (blood, ketchup) have viscosity that varies with shear rate
• Surface tension results from unbalanced molecular forces at the interface between a liquid and another substance (gas or solid)
  • Causes phenomena like capillary action and the formation of droplets
• Compressibility is significant for gases but negligible for most liquids under normal conditions
• Thermal expansion causes fluids to change volume with temperature, typically increasing for gases and liquids
• Vapor pressure is the pressure at which a liquid and its vapor are in equilibrium at a given temperature

Thermodynamic Systems and Processes

• A thermodynamic system is a region of the universe under study, separated from its surroundings by a boundary
  • Closed systems allow energy but not mass transfer, while open systems allow both
• Thermodynamic equilibrium occurs when a system's properties remain constant over time
  • Thermal, mechanical, and chemical equilibrium must be achieved
• Processes describe the path a system takes from one equilibrium state to another
  • Isothermal processes occur at constant temperature
  • Isobaric processes maintain constant pressure
  • Isochoric (isovolumetric) processes have constant volume
  • Adiabatic processes allow no heat transfer with the surroundings
• Reversible processes can be reversed without any net change to the system or surroundings
  • Irreversible processes involve energy dissipation and cannot be fully reversed
• Work is done when a system expands or contracts against an external pressure
  • For a quasistatic process, $W = \int P dV$
• Heat transfer occurs due to temperature differences and can be quantified using specific heat capacities

Equations of State

• Equations of state describe the relationship between pressure, volume, temperature, and composition for a substance
• Ideal Gas Law is the simplest equation of state, applicable to gases at low densities and high temperatures
  • Assumes no intermolecular forces and negligible molecular volume
• Van der Waals equation modifies the Ideal Gas Law to account for molecular size and attraction
  • $\left(P + \frac{a}{V_m^2}\right)\left(V_m - b\right) = RT$, where $a$ and $b$ are substance-specific constants
• Virial equation expresses the compressibility factor $(Z)$ as a power series in pressure or density
  • Useful for describing real gas behavior at moderate pressures
• Cubic equations of state (Peng-Robinson, Soave-Redlich-Kwong) are widely used in chemical engineering for their accuracy and computational efficiency
• Tabulated data and empirical correlations are often used for liquids and dense fluids due to the complexity of intermolecular interactions

Energy Transfer and Conservation

• Internal energy $(U)$ is the sum of the kinetic and potential energies of the particles in a system
  • Function of temperature, pressure, and composition
• First Law of Thermodynamics states that the change in internal energy equals the heat added minus the work done
  • $\Delta U = Q - W$ for a closed system
• Enthalpy $(H)$ is a state function defined as $H = U + PV$
  • Represents the total heat content of a system
  • For isobaric processes, change in enthalpy equals heat transferred
• Heat capacity quantifies the amount of heat required to change a substance's temperature
  • Specific heat capacity $(c)$ is heat capacity per unit mass
  • $Q = mc\Delta T$ for a constant specific heat
• Latent heat is the energy absorbed or released during a phase change at constant temperature
  • Latent heat of fusion for solid-liquid transitions and latent heat of vaporization for liquid-gas transitions
• Heat transfer occurs via conduction, convection, and radiation
  • Conduction is heat transfer through a solid or stationary fluid due to temperature gradients
  • Convection involves heat transfer by the bulk motion of a fluid
  • Radiation is the emission of electromagnetic waves from a surface due to its temperature

Applications in Engineering

• Fluid mechanics principles are essential for designing and optimizing piping systems, pumps, and valves
  • Pressure drop, flow rate, and power requirements must be considered
• Heat exchangers transfer thermal energy between fluids at different temperatures
  • Designed using principles of heat transfer and fluid mechanics to maximize efficiency
• Power cycles (Rankine, Brayton) convert heat into mechanical work using a working fluid
  • Efficiency is limited by the Second Law of Thermodynamics
• Refrigeration and air conditioning systems remove heat from a low-temperature reservoir and reject it to a high-temperature reservoir
  • Coefficient of Performance (COP) quantifies the efficiency of these systems
• Combustion processes involve the rapid oxidation of a fuel, releasing heat and products of combustion
  • Adiabatic flame temperature and chemical equilibrium are key concepts
• Psychrometrics studies the thermodynamic properties of moist air, crucial for HVAC design
  • Humidity, dew point, and wet-bulb temperature are important parameters
• Compressible flow analysis is necessary for high-speed applications like jet engines and supersonic aircraft
  • Mach number, shock waves, and choked flow are significant phenomena

Problem-Solving Techniques

• Identify the system and surroundings, specifying the type of system (open, closed, isolated)
• Determine the relevant properties and processes, making appropriate assumptions and simplifications
• Apply the conservation laws (mass, energy) and equations of state to the problem
  • First Law of Thermodynamics: $\Delta U = Q - W$ for a closed system
  • Steady-flow energy equation for open systems: $\Delta h + \Delta ke + \Delta pe + q + w = 0$
• Use property tables, charts, or equations of state to find necessary thermodynamic properties
  • Interpolate between values when needed
• Solve equations systematically, checking units and orders of magnitude for consistency
• Analyze the results critically, considering the implications and limitations of the assumptions made
• Validate the solution using alternative methods or by comparing it to known cases
• Communicate the results effectively using appropriate terminology, units, and significant figures