Energy Analysis of Closed Systems

Chapter 4: Energy Analysis of Closed Systems (Control Mass)

Goal

  • Identifying sources of energy interactions.
  • Writing energy balances in thermodynamic processes.

Introduction

  1. State the conservation of energy principle (First Law of Thermodynamics): Energy cannot be created or destroyed; it can only change forms.
  2. Write an energy balance:
    • For a general system undergoing any process.
  3. Write energy balance on unit-mass basis and unit-time basis (rate-form basis) for a general system undergoing any process.
  4. Identify the energies causing the system to change.

Objectives

  1. Identify energy changes within the system.
  2. Write the energy balance in terms of all the energies causing the change and the energy changes within the system.
  3. Write a unit-mass basis and unit-time basis (rate-form) energy balance concerning all the energies causing the change and internal energy changes within the system.
  4. State conditions for stationary closed systems and rewrite the energy balance and unit-mass basis energy balance for stationary closed systems.
  5. Apply the energy conservation principle for a stationary closed system undergoing an adiabatic process; discuss its physical interpretation.
  6. Apply energy conservation principle for a stationary closed system undergoing isochoric, isothermal, cyclic, and isobaric processes; discuss physical interpretations.
  7. Define specific heat and state its significance in determining internal energy and enthalpy change for ideal gases, liquids, and solids.
  8. Use the energy balance for problem solving.

The First Law of Thermodynamics

  • Definition: The First Law provides a sound basis for studying the relationships among various forms of energy and energy interactions.
  • Core Principle: The first law states that energy can be neither created nor destroyed during a process; it can only change forms.
  • Statement for Adiabatic Processes: For all adiabatic processes between two specified states of a closed system, the net work done is the same regardless of the nature of the closed system and the details of the process.

Energy Transfer Examples

  • Example 1:

    • Scenario: Baked potato in an oven.
    • When heat is transferred to the potato, the energy increases. For a closed system ignoring mass transfer, the energy increase equals the heat transfer amount.

  • Example 2:

    • Scenario: Heating water in a covered pan.
    • Data: 15 kJ heat transferred to the water, 3 kJ lost to surrounding air.
    • Energy Change: The net increase in energy of the water is 12 kJ.

  • Example 3:

    • Scenario: Heat and work interactions simultaneously.
    • A system gains 12 kJ of heat and 6 kJ of work done on it; total energy increase is 18 kJ.

Energy Transfer - Heat Transfer

  • Various states:
    • Example involves energy transfers to and from systems, indicated through data on temperature and pressure variations such as steam properties at different states.

Work Done in Energy Transfer

  • Boundary Work (Moving Boundary Work):
    • Expansion and compression in a piston-cylinder device.
    • Positive boundary work when the gas expands and negative during compression.
  • Quasi-Equilibrium Process:
    • Remains nearly in equilibrium at all times.
  • Graphical Representation: The area under a process curve on a P-V diagram represents boundary work.

First Law – Energy Transfer Mechanisms

  • Three Forms of Transfer:
    1. Heat (Q)
    2. Work (W)
    3. Mass flow (m)

Energy Changes Related to Energy Transfer

  1. Heat as a Cause: Changes system properties (E, P, T, V) related to heat input/output.
  2. Work as a Cause: Changes system properties (E, P, T, V) related to work input/output.
  3. Mass Transfer as a Cause: Changes in energy states (E, P, T, V) involve mass entering/exiting the system.
  4. Dynamic Energies: Their roles in energy transfer through expansion/contraction work.

Energy Balance for Closed Systems

  • Energy Balance Principle: The amount of energy causing change must equal the change in system energy.
    • E_{in} - E_{out} = riangle E_{sys}, ext{ kJ}
  • Rate Form Energy Balance:
    • Energy in per unit time should balance against energy out and energy changes in the system.
  • Unit-mass Basis Energy Balance: Similar format as above but expressed per unit mass.

Specific Heat

  • Definition of Specific Heat: Energy required to raise the temperature of a unit mass of a substance by one degree.
    • C_v at constant volume; C_p at constant pressure.
  • For gases, these values vary with temperature and help calculate changes in internal energy and enthalpy.
  • Average specific heats can be approximated over small temperature changes.

Energy Changes in Solids and Liquids

  • Considered Incompressible: Specific volume remains constant, thus simplifying calculations.
  • Energy Equations for Solids and Liquids: Signed as follows:
    • Change in internal energy riangle u = C_{av} (T_2 - T_1), ext{ kJ/kg}
    • Change in enthalpy riangle h = C_{av} riangle T + v riangle P, ext{ kJ/kg}

Examples and Applications

  • Example Scenarios Provided:
    • Rigid tank cooling process for liquid, energy balance in electric heating, etc.
    • Integration of tables for enthalpy calculations from known thermodynamic conditions.

Exercises and Problems

  • Practical applications of theoretical knowledge in energy balances, preparation for relevant exams (e.g. December 2016 Examination Part B)