Energy Transfer by Heat, Work and Mass

ENERGY TRANSFER BY HEAT, WORK, AND MASS

Goal

  • Identify forms of energy interactions and ways of representing it in thermodynamic processes.

Objectives

  1. Identify forms of energy interactions and ways of representing it in thermodynamic processes.
  2. Identify the types of dynamic energies interacting with a system.
  3. Distinguish the difference and relate between heat transfer and thermal energy.
  4. Write the different symbols and the conventions used to represent heat transfer.
  5. Differentiate between heat transfer and work.
  6. Write the symbols and convention used for work done.
  7. Obtain a mathematical relation representing mechanical work done for any system.
  8. Obtain the amount of work done from a P-V or P-ν graph.
  9. Write down the relationship between mass and volume flow rate.
  10. Obtain a mathematical relation representing mass flow rate in terms of mass velocities and the system’s inlet or exit area.
  11. Write the specific energy carried by a flowing mass.
  12. Use all mathematical relations and graphing skills to solve problems involving interaction energies.

Types of Energy

  • Dynamic Interactions:
    • Heat, Q
    • Work, W
    • Energy of moving mass, E_{mass}
    • These forms cross in and out of the system’s boundary.
  • Static System Energies:
    • Internal energy, U
    • Kinetic energy, KE
    • Potential energy, PE
    • These changes occur within the system.

Introduction

  • When considering a closed adiabatic system (e.g., a sealed room with a refrigerator or fan), the only energy interaction is the electrical energy entering the room.
  • Electrical energy converted into thermal energy leads to a rise in room temperature.
    • E.g., a fan in a sealed room raises the temperature.

ENERGY TRANSFER BY HEAT

  • Definition of Heat: The form of energy that is transferred between two systems or between a system and its surroundings due to a temperature difference.
  • Example Scenarios:
    • A cold soda warms up on a table.
    • A hot baked potato cools down on the same table.
  • Thermal Equilibrium: Energy transfer occurs until thermal equilibrium is established, moving from higher to lower temperatures.

Heat Transfer

  • Definition of Heat Transfer: Energy in transition due to temperature difference, not associated with mass transfer.
    • Energy is recognized as heat only when crossing the system boundary.
  • Key Equations:
    • Heat transfer to a system: ext{+ } ext{d}Q = Q_{in}
    • Heat transfer from a system: ext{- } ext{d}Q = Q_{out}
    • Heat transfer per unit mass: q = rac{Q}{m} (in unit: kJ/kg)
    • Rate of heat transfer: Q = rac{Q}{t} (in units: kJ/s = kW)
    • Adiabatic Process: ext{d}Q = 0. No heat transfer occurs between the system and its surroundings.

Heat Transfer Examples and Calculations

  • Isothermal Process: Monitored heat transfer during constant temperature conditions; involves observing systems at known pressure and temperature states.
  • Schematic and Symbols:
    • For total heat entering: Q_{in} = 100 ext{ kJ}, m = 5 ext{ kg}, q_{in} = rac{Q_{in}}{m}
    • For total heat leaving: Q_{out} = 20 ext{ kJ}, m = 5 ext{ kg}, q_{out} = rac{Q_{out}}{m}
    • Net Heat Transfer: Q_{net} = Q_{in} - Q_{out}

ENERGY TRANSFER BY WORK

  • Definition of Work: The energy transfer associated with a force acting through a distance.
    • Examples of work interactions include a rising piston or rotating shaft.
  • Work Sign Convention:
    • Heat transfer to a system and work done on a system are positive; heat transfer from a system and work done by a system are negative.
  • Symbols and Conventions:
    • Electrical work when N coulombs of charge move through a potential difference V yields electrical work done.
  • Mechanical Work Equation:
    • Work done is represented as W = F imes d, where F is force and d is distance.

Mechanical Work and Flow Work

  • Moving Boundary Work: Work associated with expansion or compression of gas in a piston-cylinder device.
  • Boundary Work Calculation:
    • ext{W}_{b} = ext{F} imes ext{d}s; as dV changes.
  • Flow Work: Required to maintain fluid flow; W_{f} = P imes V, where P is pressure and V is volume.
  • Total Energy of a Flowing Fluid:
    • Total energy consists of three parts for a non-flowing fluid and four parts for a flowing fluid:
    • h = u + Pv for a non-flowing fluid.
    • Also includes flow work for a flowing fluid.

Energy Analysis of Steady-Flow Systems

  • Operational under steady conditions where the mass and energy content of a control volume remains constant.
  • Mass Conservation in Flow:
    • m_{in} - m_{out} = 0 under steady-state, mass must be conserved.

Exercises

  • Example Exercise: An insulated electric oven is heated through its element. Determine if this is a heat or work interaction.
  • For the second exercise regarding just the air in the oven, assess the nature of energy interaction again.

Conclusion

  • Understanding the principles of energy transfer through heat, work, and mass is crucial for analyzing thermodynamic systems and processes efficiently.
  • Familiarity with specific terms, equations, and conditions helps in solving related thermodynamic problems, which are prevalent across multiple engineering fields.