🦫Intro to Chemical Engineering Unit 4 – Energy Balances

Energy balances are a fundamental concept in chemical engineering, applying the conservation of energy principle to analyze systems and processes. They involve accounting for all energy entering, leaving, and accumulating within a system, considering various forms like heat, work, and mass flow. Understanding energy balances is crucial for designing and optimizing real-world applications such as power plants, refrigeration cycles, and chemical reactors. Key concepts include the First Law of Thermodynamics, closed vs. open systems, and steady-state processes, which form the basis for solving complex engineering problems.

Study Guides for Unit 4

4.1

First law of thermodynamics

4 min read

4.2

Energy balance calculations

6 min read

4.3

Enthalpy and heat capacity

4 min read

4.4

Heat of reaction and heat of formation

4 min read

4.5

Energy balance for reactive systems

4 min read

Key Concepts and Definitions

Energy the capacity to do work or transfer heat
Thermodynamics the study of energy and its transformations
System a specific region or quantity of matter under study
Surroundings everything external to the system
- Can exchange energy and/or mass with the system
State variables properties that describe the state of a system (temperature, pressure, volume)
Process a change in the state of a system due to energy transfer or work
Equilibrium a state where no changes occur in the system properties over time
- Thermal equilibrium: no temperature gradient
- Mechanical equilibrium: no pressure gradient

Energy Balance Fundamentals

Conservation of energy principle energy cannot be created or destroyed, only converted from one form to another
Energy balance an accounting of all energy entering, leaving, and accumulating within a system
- Applies the conservation of energy principle
Reference states chosen states for assigning a value of zero to a specific property (enthalpy, entropy)
Heat transfer energy transfer due to a temperature difference between the system and surroundings
- Occurs through conduction, convection, or radiation
Work energy transfer due to a force acting over a distance
- Includes expansion/compression work, shaft work, and electrical work
Internal energy a state function representing the total kinetic and potential energy of a system
Enthalpy a state function equal to the sum of internal energy and the product of pressure and volume ( $H = U + PV$ )

Types of Energy in Chemical Systems

Kinetic energy energy associated with the motion of an object ( $KE = \frac{1}{2}mv^2$ )
Potential energy energy stored due to an object's position or configuration
- Gravitational potential energy: $PE = mgh$
- Chemical potential energy: energy stored in chemical bonds
Thermal energy (heat) energy associated with the random motion of particles in a substance
Mechanical energy the sum of kinetic and potential energy in a system
Chemical energy energy stored in chemical bonds and released or absorbed during chemical reactions
Electrical energy energy associated with the flow of electric charges
Nuclear energy energy released during nuclear reactions (fission or fusion)

First Law of Thermodynamics

States that the change in internal energy of a system equals the heat added minus the work done by the system ( $\Delta U = Q - W$ )
Applies the conservation of energy principle to thermodynamic systems
Heat ( $Q$ ) is positive when added to the system and negative when removed from the system
Work ( $W$ ) is positive when done by the system on the surroundings and negative when done on the system by the surroundings
For a cyclic process, the change in internal energy is zero ( $\Delta U = 0$ $Δ U = 0$ )
- Heat added equals work done ( $Q = W$ )
Enthalpy change ( $\Delta H$ ) is often used in place of internal energy change for processes at constant pressure

Closed vs. Open Systems

Closed system (control mass) a fixed amount of mass with no exchange of matter with the surroundings
- May exchange energy (heat and work) with the surroundings
Open system (control volume) a region in space with mass flowing in and out
- Exchanges both energy and mass with the surroundings
Isolated system does not exchange energy or mass with the surroundings
Adiabatic system does not exchange heat with the surroundings but may exchange work
Steady-state system has no change in properties over time (mass flow rates, temperatures, pressures remain constant)
- Applicable to many open systems (heat exchangers, turbines, pumps)

Energy Balance Equations and Calculations

General energy balance equation: $\Delta U = Q - W + \sum m_i(h_i + \frac{v_i^2}{2} + gz_i) - \sum m_e(h_e + \frac{v_e^2}{2} + gz_e)$ $Δ U = Q - W + \sum m_{i} (h_{i} + \frac{v _{i}^{2}}{2} + g z_{i}) - \sum m_{e} (h_{e} + \frac{v _{e}^{2}}{2} + g z_{e})$
- $\Delta U$ : change in internal energy
- $Q$ : heat added to the system
- $W$ : work done by the system
- $m_i$ , $m_e$ : mass flow rates in and out
- $h_i$ , $h_e$ : specific enthalpies in and out
- $v_i$ , $v_e$ : velocities in and out
- $z_i$ , $z_e$ : elevations in and out
Simplified energy balance for a closed system: $\Delta U = Q - W$
Steady-state, steady-flow energy balance: $0 = \dot{Q} - \dot{W} + \sum \dot{m}_i(h_i + \frac{v_i^2}{2} + gz_i) - \sum \dot{m}_e(h_e + \frac{v_e^2}{2} + gz_e)$ $0 = \dot{Q} - \dot{W} + \sum \overset{m}{˙}_{i} (h_{i} + \frac{v _{i}^{2}}{2} + g z_{i}) - \sum \overset{m}{˙}_{e} (h_{e} + \frac{v _{e}^{2}}{2} + g z_{e})$
- $\dot{Q}$ , $\dot{W}$ , $\dot{m}$ : rates of heat, work, and mass flow
Enthalpy balance for a steady-state, steady-flow process: $0 = \dot{Q} - \dot{W}_s + \sum \dot{m}_ih_i - \sum \dot{m}_eh_e$ $0 = \dot{Q} - \dot{W}_{s} + \sum \overset{m}{˙}_{i} h_{i} - \sum \overset{m}{˙}_{e} h_{e}$
- $\dot{W}_s$ : rate of shaft work

Real-World Applications

Power plants use energy balances to optimize efficiency and minimize waste heat
- Boilers, turbines, condensers, and pumps are analyzed as open systems
Refrigeration cycles (air conditioners, refrigerators) rely on energy balances to calculate heat removal and work input
- Evaporators, compressors, condensers, and expansion valves are treated as open systems
Heat exchangers (shell-and-tube, plate) are designed using energy balances to determine heat transfer rates and outlet temperatures
Chemical reactors (batch, continuous stirred-tank, plug-flow) use energy balances to account for heat of reaction and temperature changes
Distillation columns employ energy balances to calculate reboiler and condenser duties, as well as stage temperatures and compositions
Fuel cells and batteries are analyzed using energy balances to determine efficiency and power output

Common Pitfalls and Tips

Ensure consistent units throughout calculations (SI or English)
Pay attention to sign conventions for heat and work (positive or negative)
Clearly define the system and surroundings for each problem
Identify the type of system (closed, open, steady-state) to apply the appropriate energy balance equation
Account for all forms of energy entering and leaving the system (heat, work, mass flow)
Use reference states consistently when calculating changes in properties (enthalpy, entropy)
Double-check that the energy balance equation is satisfied (inputs = outputs + accumulation)
Simplify the energy balance equation when appropriate (neglect kinetic/potential energy, assume steady-state)