Reading_thermo_1st 2nd law

First Law Applied to Flow Processes

5.1 Control Volume

• First Law Equation: For any system and in any process, the first law can be expressed as:

  • Q = AE + W

  • where E represents all forms of energy stored in the system.

• For a pure substance, total energy E is given by:

  • E = Ek + Ep + U

  • where Ek is Kinetic Energy, Ep is Potential Energy, and U is residual energy due to molecular structure.

• The equation with mass transfer is:

  • Q = A Ek + A Ep + AU + W

• Open System: A system allowing mass transfer across its boundary; most engineering devices like steam turbines are open systems.

• Example: In a steam turbine, steam enters at high pressure, does work on the rotor, and exits low pressure. Energy changes must be analyzed through the turbine.

5.2 Steady Flow Process

• Definition: A steady flow process where mass and energy flow rates across the control surface are constant.

• Conditions:

  • Steady state implies thermodynamic properties at a specific location do not change over time, although they can vary spatially.

5.3 Mass and Energy Balance in Steady Flow Process

• Diagram: Refers to a steady flow system where:

  • One fluid stream enters and exits the control volume (see Fig. 5.2).

• Key Quantities:

  • A₁, A₂: Cross-section areas (m²)

  • W₁, W₂: Mass flow rates (kg/s)

  • P₁, P₂: Absolute pressures (N/m²)

  • D₁, D₂: Specific volumes (m³/kg)

  • U₁, U₂: Specific internal energies (J/kg)

  • V₁, V₂: Velocities (m/s)

  • Z₁, Z₂: Elevations (m)

  • Q: Net rate of heat transfer (J/s)

  • W: Net rate of work transfer (J/s)

5.3.1 Mass Balance

• Conservation of Mass: If no accumulation occurs within the control volume:

  • W₁ = W₂, or A₁ V₁ = A₂ V₂ (Equation of continuity).

5.3.2 Energy Balance

• Work Transfer Types: Two types - external work and flow work.

  • External work: shaft work or electrical work.

  • Flow work: displacement work done by the fluid.

• Total Work Transfer:

  • W = (p₁ V₁ dm) + (p₂ V₂ dm)

• Conservation of energy states that total energy inflow equals total energy outflow:

  • Total inflow = Total outflow

5.4 Examples of Steady Flow Processes

5.4.1 Nozzle and Diffusor

• Nozzle: Converts pressure energy to kinetic energy.

• Diffusor: Converts kinetic energy to pressure energy. The equations reduce under specific assumptions (e.g., negligible P.E.).

5.4.2 Throttling Device

• Throttling Process: Significant pressure drop; changes in P.E. are often negligible, leading to h₁ = h₂.

5.4.3 Turbine and Compressor

• Turbine: Does work on fluid; energy loss related to enthalpy change.

• Compressor: Requires work input, increasing enthalpy.

5.4.4 Heat Exchanger

• Function: Transfers heat between two fluids without external work; simplifies to specific energy balances.

5.5 Comparison of S.F.E.E. with Euler and Bernoulli Equations

• The steady flow energy equation (S.F.E.E.) compares with Euler's and Bernoulli's equations where Bernoulli's is a special case of S.F.E.E. for inviscid flow.

5.6 Variable Flow Processes

• Definition: Flow processes like filling gas cylinders can be analyzed through control volume techniques, with mass accumulation described mathematically.

• Energy and mass balances apply as changes in control volumes occur.

5.7 Example of a Variable Flow Problem

• Bottle Filling Example: Explores energy balances and flow rates during the gas accumulation in a bottle.

5.8 Discharging and Charging a Tank

• Describes the energy transfer mechanics when a tank discharges fluid; uses specific work and mass flow terms to illustrate the principles.

5.9 Solved Examples

• Real-world applications reinforce the applicability of energy balances and mass balances in steady and variable flow processes, calculating efficiencies and results from provided parameters.

Review Questions

• Explore key concepts such as system vs control volume, the definition and implications of steady flow processes, and details of mass vs energy balance in practical applications.