Thermodynamics Lecture Notes

Types of Energy

1. Stored Energy
   • Kinetic Energy (KE) ( E_k = \frac{1}{2}mv^2 )
   • Potential Energy (PE) ( E_p = mgh )
   • Internal Energy
   • Chemical Energy
   • Magnetic Energy
2. Transit Energy
   • Not discussed in detail
   • Work Transfer
   • Heat Transfer

Heat Transfer

• Definition: Energy interaction responsible for temperature or phase change.
• Types:
  • Sensible Heat
    • Causes temperature change
    • Equation: ( Q = mc\Delta T )
  • Latent Heat
    • Causes phase change
    • Phase change occurs at constant temperature.
    • Equation: ( Q = mL )

First Law of Thermodynamics

• For Closed System:
  • Cycle: ( \Delta U = 0; Q_{1-2}=W_{1-2} )
  • Process: Focus on internal energy changes ( Q_{in} - W_{out} = \Delta U )

Sign Convention for Heat Transfer

• Heat added to the system: Positive
• Heat rejected by the system: Negative
• Units: KiloJoules (kJ)

Specific Heat Capacity

• Specific Heat at Constant Volume (( C_v )): ( Q_v = mC_v\Delta T )
• Specific Heat at Constant Pressure (( C_p )): ( Q_p = mC_p\Delta T )
• Relationship: ( C_p - C_v = R )
• For Ideal Gas: ( C_p / C_v = \gamma ) where ( \gamma ) is the adiabatic index.

Understanding Internal Energy

• Definition: Energy stored due to molecular activities (translational, rotational, vibrational).
• For Ideal Gas: Internal energy is a function of temperature only.
• Equation: ( U = mC_v T )

Enthalpy (H)

• Definition: ( H = U + PV )
• Represents total energy in an open system.

Perpetual Motion Machine of First Kind (PMM1)

• Impossible device: Produces work without energy input, violating the first law of thermodynamics.

Steady Flow Energy Equation (SFEE)

• First Law for Open System (Steady Flow):( E_{in} = E_{out} + \Delta E_{storage} ) where ( \Delta E_{storage} = 0 ) at steady state.
• Equation: ( \dot{m_i}(h_i + \frac{v_i^2}{2} + g z_i) + Q_{in} = \dot{m_e}(h_e + \frac{v_e^2}{2} + g z_e) + W_{out} [: with mass flow rate ]

Common Applications of SFEE

• Turbine: ( W_{cv} = \dot{m} (h_i - h_e) )
• Compressor: ( W_{cv} = \dot{m} (h_e - h_i) )
• Heat Exchanger:
  • Total Energy Conservation with Mixing Fluids: ( \sum \dot{m_{in}} h_{in} = \sum \dot{m_{out}} h_{out} )
  • Heat Transfer Calculation: Heat rejected = Heat absorbed.
• Nozzle: Increase kinetic energy of the fluid. ( v_e = \sqrt{2c_p (T_i - T_e)} )
• Diffuser: Reduces speed, increases pressure and enthalpy.
• Throttling: ( h_i = h_e )

Non-Steady Flow Energy Equation (NSFEE)

• First Law for Non-Steady Flow System: ( E_{in} = E_{out} + \Delta E_{storage} )
  • Applies to processes where mass and energy rates are not constant.

Applications of NSFEE

• Charging and Discharging of Tank
  • Assumptions: Adiabatic, no work done, initial/ final conditions as specified.
  • Charging: [ \dot{m_i} h_i = m_2 u_2 ]
  • Discharging: [ m_1 u_1 = m_e h_e ]
• Mixing Process: Apply the general energy equation for flow systems ( \sum m_{in} h_{in} = \sum m_{out} h_{out} )