Thermo-Energy

Thermodynamics and Energy Balance Study Notes

Overview

• Thermodynamics: Study of energy behavior in various systems, focusing on energy storage, transfer, conversion, and equilibrium.

• Key Areas of Focus: The application of thermodynamic laws to food systems, among other applications.

• Learning Outcomes:

  • Define energy, heat, work, and entropy.

  • State the first and second laws of thermodynamics.

  • Apply energy balance principles to solve problems in food processing systems.

Four Laws of Thermodynamics

Zeroth Law

• Definition: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

• Implication: Establishes the concept of temperature.

First Law of Thermodynamics

• Definition: Conservation of Energy.

  • Energy cannot be created or destroyed; it only changes from one form to another.

  • Consequence: If a system gains or loses energy, the surroundings must experience an equivalent loss or gain in energy.

Second Law of Thermodynamics

• Definition: Direction of energy processes and the concept of entropy.

  • Entropy (S): Measures the unavailable energy for doing work in a system.

  • Key Principle: The disorder of a system tends to increase, and energy conversions lead to less usable energy.

  • Phenomena of irreversibility:

  • Heat does not spontaneously flow from colder to hotter areas or gases in a chamber do not revert to individual gas entities.

  • Mathematical Expression: $dS = \frac{dQ}{T}$

Third Law of Thermodynamics

• Statement: A perfect crystalline solid has zero entropy at absolute zero temperature (-273°C).

• Note: Absolute zero is unattainable in practice.

Energy Concepts

Energy

• Nature: Energy is a scalar physical quantity that can exist in different forms.

Types of Energy

1. Potential Energy (PE)

   • Resultant from gravitational forces on an object of mass ‘m’.

   • Formula: $E_{Potential} = mgh$

2. Kinetic Energy (KE)

   • Associated with the movement of an object with mass ‘m’.

   • Formula: $E_{Kinetic} = \frac{1}{2}mv^2$

3. Internal Energy (EInternal)

   • Dependent on pressure and temperature.

   • Composed of potential energy from chemical bonds and kinetic energy from particle motions.

Total Energy of a System

• Formula for Total Energy:
  $E<em>{Total} = E</em>{Potential} + E<em>{Kinetic} + E</em>{Electrical} + E<em>{Magnetic} + E</em>{Internal}$

• Simplification for food processing:
  $E<em>{Total} = E</em>{Potential} + E<em>{Kinetic} + E</em>{Internal}$

Conservation of Energy

• In an isolated system, energy remains constant; it can only change forms without being destroyed or created.

Energy Transfer by Heat

Modes of Heat Transfer

1. Convection

2. Conduction

3. Radiation

Heat Transfer Parameters

• Heat Capacity (C):
  $C = \frac{Q}{\Delta T}$

• Specific Heat Capacity (Cp or Cv):

  • At constant pressure (Cp):
    $C_p = \frac{Q}{m \Delta T}$

  • At constant volume (Cv):

• Energy conversion:

  • Caloric conversion:

  • $1 ext{ calorie} = 4.1855 ext{ J}$

  • Cp of Water: Given as 4.1855 J/(g.K) at 15°C and 1 atm.

Heat Transfer Calculation

• Formula:
  $Q = m \cdot C_p \cdot \Delta T$

Enthalpy

• Definition: A thermodynamic potential expressing energy per unit thermodynamic variable.

• Formula for Enthalpy (H):
  $H = E_{Internal} + PV$

• For heat transfer applications:
  $\Delta H = q = m \cdot C_p \cdot \Delta T$

• Reference enthalpy fixed at a specific temperature (e.g., enthalpy of some food products at -40°C is set to zero).

Energy Balance in Systems

Energy Balance Equation

• General form:
  $\Delta E = E<em>{in} - E</em>{out}$

Steady State Systems

• Assumes no change in energy over time:
  $\Delta E = 0 \Rightarrow E<em>{in} = E</em>{out}$

Open vs. Closed Systems

1. Open Systems:

   • Both mass and energy flow.

   • Work due to mass flow:
     $W = F \cdot \Delta z = P \cdot A \cdot \Delta z = P \cdot \Delta V$

   • Energy change equation:
     $\Delta E = E<em>{in} - E</em>{out} + P \cdot \Delta V$

2. Closed Systems:

   • No mass flow occurs.

   • Energy change equation:
     $\Delta E = E<em>{in} - E</em>{out} - W_{done\ on\ the\ system}$

Work Done on a Closed System

• Work due to different fields:

  • Gravitational Work:
    $W = m \cdot g \cdot (z<em>2 - z</em>1)$

  • Acceleration Work:
    $W = \frac{1}{2} m (v<em>2^2 - v</em>1^2)$

  • Pressure Work:
    $W = P(V<em>2 - V</em>1)$

Examples of Energy Balance in Food Processing

Example 1: Steam Peeling Potatoes

• Process: Steam used at a rate of 4 kg per 100 kg of unpeeled potatoes.

• **Temperatures:

  • Unpeeled Potatoes:** 17°C

  • Peeled Potatoes:** 35°C

  • Waste stream leaves at:** 60°C

• Specific Heats:

  • Unpeeled Potatoes: 3.7 kJ/(kg K)

  • Waste Stream: 4.2 kJ/(kg K)

  • Peeled Potatoes: 3.5 kJ/(kg K)

• Steam Heat Content: 2750 kJ/kg at 0°C reference temperature.

Example 2: Tubular Water Blancher for Lima Beans

• Flow Rate: 860 kg/h

• Energy Consumption: 1.19 GJ/h for blanching.

• Energy Losses: Estimated at 0.24 GJ/h due to lack of insulation.

• Total Energy Input: 2.71 GJ/h.

  • Tasks:

  • Calculate energy required to reheat water.

  • Determine percentage energy associated with each stream: energy losses, energy leaving with product, energy input.

Thermodynamics and Energy Balance Cheat Sheet

Overview

• Thermodynamics: Study of energy behavior (storage, transfer, conversion, equilibrium) in systems.

• Focus: Application of thermodynamic laws, especially in food systems.

Four Laws of Thermodynamics

Zeroth Law

• Definition: If two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other.

• Implication: Defines temperature.

First Law of Thermodynamics

• Definition: Conservation of Energy.

  • Energy cannot be created or destroyed, only changes forms.

  • System energy gain/loss equals surroundings energy loss/gain.

Second Law of Thermodynamics

• Definition: Direction of energy processes; concept of entropy.

  • Entropy (S): Measures unavailable energy for work; system's disorder tends to increase.

  • Mathematical Expression: $dS = \frac{dQ}{T}$

Third Law of Thermodynamics

• Statement: A perfect crystalline solid has zero entropy at absolute zero temperature ($-273^{\circ}C$).

Energy Concepts

Energy

• Nature: Scalar physical quantity, exists in different forms.

Types of Energy

1. Potential Energy (PE)

   • Due to gravitational forces.

   • Formula: $E_{\text{Potential}} = mgh$

2. Kinetic Energy (KE)

   • Due to movement.

   • Formula: $E_{\text{Kinetic}} = \frac{1}{2}mv^2$

3. Internal Energy (EInternal)

   • Dependent on pressure and temperature; stored in chemical bonds and particle motion.

Total Energy of a System

• Simplified for food processing: $E<em>{\text{Total}} = E</em>{\text{Potential}} + E<em>{\text{Kinetic}} + E</em>{\text{Internal}}$

Conservation of Energy

• In an isolated system, total energy remains constant.

Energy Transfer by Heat

Modes of Heat Transfer

1. Convection

2. Conduction

3. Radiation

Heat Transfer Parameters

• Heat Capacity (C): $C = \frac{Q}{\Delta T}$

• Specific Heat Capacity (Cp or Cv):

  • At constant pressure (Cp): $C_p = \frac{Q}{m \Delta T}$

  • Caloric conversion: $1\ \text{calorie} = 4.1855\ \text{J}$

  • Cp of Water: 4.1855\ \text{J/(g\cdot K)} at $15^{\circ}C$, $1\ \text{atm}$.

Heat Transfer Calculation

• Formula: $Q = m \cdot C_p \cdot \Delta T$

Enthalpy

• Definition: Thermodynamic potential, energy per unit thermodynamic variable.

• Formula: $H = E_{\text{Internal}} + PV$

• For heat transfer: $\Delta H = q = m \cdot C_p \cdot \Delta T$

• Reference enthalpy can be set to zero at a specific temperature.

Energy Balance in Systems

Energy Balance Equation

• General form: $\Delta E = E<em>{\text{in}} - E</em>{\text{out}}$

Steady State Systems

• No change in energy over time: $\Delta E = 0 \Rightarrow E<em>{\text{in}} = E</em>{\text{out}}$

Open vs. Closed Systems

1. Open Systems:

   • Both mass and energy flow.

   • Work due to mass flow: $W = P \cdot \Delta V$

   • Energy change: $\Delta E = E<em>{\text{in}} - E</em>{\text{out}} + P \cdot \Delta V$

2. Closed Systems:

   • No mass flow.

   • Energy change: $\Delta E = E<em>{\text{in}} - E</em>{\text{out}} - W_{\text{done on the system}}$

Work Done on a Closed System

• Gravitational Work: $W = m \cdot g \cdot (z<em>2 - z</em>1)$

• Acceleration Work: $W = \frac{1}{2} m (v<em>2^2 - v</em>1^2)$

• Pressure Work: $W = P(V<em>2 - V</em>1)$

Examples of Energy Balance in Food Processing

• Practical applications involve calculating energy transfers in processes like steam peeling (potatoes) or blanching (lima beans), considering specific heats, temperatures, and steam/energy inputs/losses.