3.3 Conservation of energy principle

The conservation of energy principle is a cornerstone of thermodynamics. It states that energy can't be created or destroyed, only converted or transferred. This principle forms the basis of the First Law of Thermodynamics, which quantifies energy changes in systems.

In thermodynamics, we apply this principle to closed and open systems. For closed systems, energy changes are due to heat and work. Open systems also consider mass flow. Understanding these concepts is crucial for analyzing real-world thermal processes.

Conservation of Energy in Thermodynamics

Fundamental Principle and First Law of Thermodynamics

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• The conservation of energy principle states that energy cannot be created or destroyed, only converted from one form to another or transferred between systems
• In a closed system, the total energy remains constant, and any change in the system's energy is due to energy transfer across the system boundary in the form of heat or work
• The first law of thermodynamics is a statement of the conservation of energy principle, expressing that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system
• The conservation of energy principle applies to all forms of energy, including thermal, mechanical, electrical, chemical, and nuclear energy (nuclear fission, nuclear fusion)

Energy Classification and Examples

• Energy can be classified as either stored (potential) or in transit (kinetic)
  • Examples of stored energy include chemical (fossil fuels, batteries), nuclear (uranium), and gravitational potential energy (water in a reservoir)
  • Examples of energy in transit include thermal (heat transfer), mechanical (rotating shaft), and electrical energy (current in a circuit)

Energy Balance for Systems

Closed Systems

• In a closed system, no mass crosses the system boundaries, and the change in the system's energy is solely due to heat and work interactions with the surroundings
• For a closed system undergoing a process, the change in the system's total energy (ΔE) is equal to the heat added to the system (Q) minus the work done by the system (W): $ΔE = Q - W$
• For a closed system, the change in total energy (ΔE) is equal to the change in the system's internal energy (ΔU), as there is no change in the system's kinetic or potential energy: ΔE = [ΔU = Q - W](https://www.fiveableKeyTerm:δu_=_q_-_w)

Open Systems

• In an open system, mass, as well as energy, can cross the system boundaries (steam turbine, heat exchanger)
• The conservation of energy principle must account for the energy associated with the mass flow in addition to heat and work interactions
• For an open system, the change in the system's total energy (ΔE) is equal to the heat added to the system (Q), minus the work done by the system (W), plus the energy associated with the mass entering the system (Emass,in), minus the energy associated with the mass leaving the system (Emass,out): $ΔE = Q - W + Emass,in - Emass,out$
• The energy associated with the mass flow includes the enthalpy, kinetic energy, and potential energy of the flowing matter (steam, air, refrigerant)

Applying Conservation of Energy

Energy Balance Equations for Various Processes

• The general energy balance equation for a closed system undergoing a process is: $ΔE = Q - W$, where ΔE is the change in the system's total energy, Q is the heat added to the system, and W is the work done by the system
• The energy balance equation for an open system, considering the steady-state flow process, is: $Qnet + Wnet = Σ(ṁout × hout) - Σ(ṁin × hin) + Σ(ṁout × (ve,out^2 / 2 + gze,out)) - Σ(ṁin × (ve,in^2 / 2 + gze,in))$, where Qnet is the net heat transfer rate, Wnet is the net work rate, ṁ is the mass flow rate, h is the specific enthalpy, ve is the velocity, g is the acceleration due to gravity, and ze is the elevation at the inlet (in) and outlet (out) of the system
• For a control volume with multiple inlets and outlets, the energy balance equation must account for the energy associated with each mass flow stream (power plant with multiple steam extractions)

Transient and Steady-State Processes

• In a transient (unsteady) process, the energy storage term must be included in the energy balance equation to account for the change in the system's energy over time (charging a compressed air storage tank)
• For steady-state processes, the energy storage term is zero, simplifying the energy balance equation (continuous operation of a gas turbine)

Energy Balance in Processes

Problem-Solving Approach

• Identify the system boundaries and determine whether the system is closed or open
• Determine the relevant energy interactions (heat, work, and mass flow) crossing the system boundaries
• Write the appropriate energy balance equation based on the type of system (closed or open) and the nature of the process (steady-state or transient)
• Identify the known and unknown variables in the energy balance equation
• Use the properties of the system (specific heats, enthalpies, pressures, and temperatures) to relate the unknown variables to the known variables

Interpreting Results and Checking Solutions

• Solve the energy balance equation for the desired unknown variable, such as the final temperature, heat transfer, work done, or mass flow rate
• Interpret the results and check the solution for consistency with the problem statement and physical laws
  • Verify that the units of the solution are correct and consistent with the problem
  • Check if the magnitude and sign of the solution make physical sense (positive heat transfer into the system, negative work done by the system)
  • Confirm that the solution satisfies the conservation of energy principle and the first law of thermodynamics