1.1 First Law of Thermodynamics and Energy Balance

The First Law of Thermodynamics is a fundamental principle in energy conservation. It states that energy can't be created or destroyed, only transformed. This law helps us understand how energy moves and changes in various systems, from engines to refrigerators.

Applying the First Law involves calculating work, heat, and energy interactions in thermodynamic processes. By analyzing these energy transfers, we can determine system efficiency and performance. This knowledge is crucial for optimizing energy use in real-world applications.

Thermodynamics of Systems

First Law of Thermodynamics

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• The first law of thermodynamics is a statement of the conservation of energy principle
• Energy cannot be created or destroyed, only transformed from one form to another
• For a closed system, the change in internal energy (ΔU) equals the sum of the heat (Q) added to the system and the work (W) done by the system: ΔU = Q + W
• For an open system, the change in energy (ΔE) equals the sum of the heat (Q) added to the system, the work (W) done by the system, and the net energy transfer due to mass flow across the system boundaries (ΣmΔh): ΔE = Q + W + ΣmΔh

Applying the First Law to Thermodynamic Processes

• The first law can be applied to various thermodynamic processes to determine the changes in system properties and energy interactions
  • Isothermal processes occur at constant temperature
  • Isobaric processes occur at constant pressure
  • Isochoric processes occur at constant volume
  • Adiabatic processes occur without heat transfer between the system and surroundings
• The first law can be used to analyze the performance of thermodynamic devices by evaluating the energy balance and efficiency
  • Heat engines convert thermal energy into mechanical work (internal combustion engines, steam turbines)
  • Refrigerators and heat pumps transfer thermal energy from a low-temperature reservoir to a high-temperature reservoir (air conditioners, refrigerators)

Work, Heat, and Energy Interactions

Calculating Work and Heat

• Work (W) is the energy transfer associated with a force acting through a distance
  • For a quasi-static process, work can be calculated as the product of pressure (P) and change in volume (ΔV): W = -PΔV
  • Negative sign indicates work done by the system on the surroundings
• Heat (Q) is the energy transfer due to a temperature difference between a system and its surroundings
  • Heat can be calculated using the specific heat capacity (c) and the change in temperature (ΔT): Q = mcΔT
  • Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree (water, air)

Internal Energy, Enthalpy, and Ideal Gas Behavior

• The change in internal energy (ΔU) can be determined using the first law of thermodynamics, considering the work and heat interactions in a process: ΔU = Q + W
• For an ideal gas, the change in internal energy depends only on the change in temperature and can be calculated using the specific heat at constant volume (cv): ΔU = ncvΔT
  • Ideal gases follow the ideal gas law: PV = nRT (air at room temperature and pressure)
• The change in enthalpy (ΔH) is a measure of the total heat content of a system and can be calculated using the specific heat at constant pressure (cp): ΔH = ncpΔT
  • Enthalpy is useful for analyzing processes at constant pressure (isobaric processes)

Graphical Representations of Thermodynamic Processes

• The work, heat, and energy interactions can be represented graphically on pressure-volume (P-V) and temperature-entropy (T-s) diagrams to visualize the thermodynamic processes
  • P-V diagrams show the relationship between pressure and volume during a process (isothermal, isobaric, isochoric, adiabatic)
  • T-s diagrams show the relationship between temperature and entropy during a process (Carnot cycle, Rankine cycle)
• Graphical representations help in understanding the direction and magnitude of energy transfers and the net work done during a thermodynamic cycle

Energy Balance Calculations

Applying Energy Balance to Thermodynamic Systems

• Energy balance calculations involve applying the first law of thermodynamics to determine the net change in energy for a system, considering all energy interactions (work, heat, and mass flow)
• For a closed system undergoing a cyclic process, the net change in internal energy is zero (ΔU = 0), and the net work done by the system equals the net heat added to the system: Wnet = Qnet
  • Cyclic processes return the system to its initial state (Carnot cycle, Rankine cycle)
• For an open system at steady state, the net change in energy is zero (ΔE = 0), and the energy balance equation simplifies to: 0 = Q + W + Σmh
  • Steady-state systems have constant properties over time (power plants, refrigeration systems)

Energy Balance in Thermodynamic Devices

• Energy balance calculations can be applied to various thermodynamic devices to determine the energy transfer and efficiency of these components
  • Heat exchangers transfer thermal energy between two fluids at different temperatures (radiators, condensers)
  • Turbines convert the energy of a flowing fluid into mechanical work (steam turbines, gas turbines)
  • Compressors increase the pressure of a fluid by doing work on the system (air compressors, refrigerant compressors)
  • Nozzles convert the pressure energy of a fluid into kinetic energy (jet engines, rocket nozzles)

Efficiency and Performance of Thermodynamic Systems

• The efficiency of a heat engine (ηth) is defined as the ratio of the net work output to the heat input: ηth = Wnet/Qin
  • The efficiency of a heat engine is always less than 100% due to irreversibilities and heat losses (Carnot efficiency)
• The efficiency of a refrigerator or heat pump (COP) is defined as the ratio of the desired energy transfer to the work input
  • COPref = Qc/Win for refrigerators, where Qc is the heat removed from the cold reservoir
  • COPhp = Qh/Win for heat pumps, where Qh is the heat delivered to the hot reservoir
• Energy balance calculations can be used to optimize the performance of thermodynamic systems by minimizing energy losses and maximizing the desired energy transfer
  • Improving insulation, reducing friction, and increasing component efficiencies can enhance overall system performance

Forms of Energy and Transformations

Types of Energy

• Kinetic energy (KE) is the energy associated with the motion of an object, given by: KE = (1/2)mv^2, where m is the mass and v is the velocity of the object
  • Examples include a moving car, a flowing fluid, or a rotating turbine
• Potential energy (PE) is the energy associated with the position or configuration of an object in a force field
  • Gravitational potential energy depends on the height of an object in a gravitational field (hydroelectric dams)
  • Elastic potential energy is stored in deformed elastic materials (springs, rubber bands)
• Internal energy (U) is the sum of the kinetic and potential energies of the particles within a system
  • Internal energy depends on the temperature, pressure, and volume of the system
  • Internal energy changes during thermodynamic processes due to heat and work interactions

Chemical and Electrical Energy

• Chemical energy is the energy stored in the bonds between atoms in a molecule
  • Chemical energy can be released or absorbed during chemical reactions (combustion, photosynthesis)
  • Fuels such as gasoline, natural gas, and coal store chemical energy that can be converted to thermal energy through combustion
• Electrical energy is the energy associated with the movement of charged particles, such as electrons in a circuit
  • Electrical energy can be converted to other forms of energy, such as mechanical energy in motors or thermal energy in resistors
  • Batteries store chemical energy and convert it to electrical energy to power devices

Thermal and Mechanical Energy

• Thermal energy is the energy associated with the random motion of particles in a substance
  • Thermal energy is related to the temperature of the system
  • Heat is the transfer of thermal energy between systems due to a temperature difference
• Mechanical energy is the sum of the kinetic and potential energies of an object or system
  • Mechanical energy can be converted to other forms of energy through work (turbines, engines)
  • Mechanical energy is conserved in the absence of non-conservative forces such as friction

Energy Transformations and Conservation

• The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another
• Energy transformations occur in various thermodynamic processes
  • Heat engines convert thermal energy to mechanical energy (internal combustion engines, steam turbines)
  • Refrigerators and heat pumps convert mechanical energy to thermal energy to transfer heat from a low-temperature reservoir to a high-temperature reservoir
  • Electric generators convert mechanical energy to electrical energy (wind turbines, hydroelectric generators)
  • Solar cells convert solar energy (electromagnetic radiation) to electrical energy (photovoltaic panels)
• Understanding energy transformations is crucial for designing and analyzing efficient and sustainable energy systems