Week 8 - Thermodynamics: Work, Energy, and the Human Body

Learning Outcomes

• Thermal Concepts:

  • Understand thermal energy, heat, and the mechanical equivalent of heat.

  • Familiarity with specific heat capacity, latent heat, heat of fusion, and vaporization.

• Heat Transfer Mechanisms:

  • Describe heat transfer by conduction, convection, radiation, and evaporative cooling.

• Thermodynamics:

  • Understand the First Law of Thermodynamics, heat, and energy flows in the human body.

• Metabolism:

  • Describe and quantify Metabolic and Basal Metabolic Rate (BMR) and its relation to oxygen consumption.

Energy and Human Life

• Chemical Energy Sources:

  • Carbohydrates, fats, and others provide energy through metabolism.

• ATP:

  • Body's "energy currency".

• Heat and Work Equation:

  • AU = E{in} - Q{out} - W

Mechanical Equivalent of Heat

• Heat viewed as a transfer of energy:

  • Early theories: Heat as caloric fluid.

  • Joule's experiment (18th - 19th century) showed heat is related to energy transfer.

• Conversions:

  • 1 ext{ cal} = 4.186 ext{ J}

  • 1 ext{ kcal} ext{ (Calorie)} ext{ used for food energy}

Thermal Energy vs. Heat

• Internal Energy:

  • Combines chemical and thermal energy.

  • Thermal energy consists of atomic and molecular kinetic and potential energy.

• Heat (Q):

  • Energy transferred due to temperature difference.

  • Not to be confused with fluid volume flow rate.

Specific Heat Capacity and Phase Change

• Specific Heat Formula:

  • Q = mc∆T

    Where:

    • Q = heat energy (in joules)

    • m = mass of the substance (in kilograms)

    • c = specific heat capacity (in joules per kilogram per degree Celsius)

    • ∆T = change in temperature (in degrees Celsius)

  • Where c depends on substance (e.g.,

  • Water: 4186 J kg^{-1} K^{-1}

  • Copper: 390 J kg^{-1} K^{-1}).

• Latent Heat:

  • Required for phase changes without temperature change.

  • LF ext{ (fusion)} = 334 ext{ kJ/kg}, LV ext{ (vaporization)} = 2260 ext{ kJ/kg}.

Heat Transfer Mechanisms

• Conduction:

  • Energy transfer through molecular collisions, dependent on temperature gradient.

• Convection:

  • Heat transfer via mass movement of molecules (e.g., blood in the body).

• Radiation:

  • Emission of electromagnetic waves due to electron oscillations.

  • Power radiated: rac{ riangle Q}{ riangle t} = e imes \sigma A T^4 where \eta = 5.67 imes 10^{-8} Wm^{-2}K^{-4}

The First Law of Thermodynamics

• Law of Conservation of Energy:

  • Total energy is constant; can be transformed or transferred but not created or destroyed.

• Equation:

  • riangle U = Q_{in} - W

  • Implications in metabolism: Internal energy change relates to heat and work performed.

Metabolism and BMR

• Metabolic Rate:

  • Reflects oxygen consumption; approximate energy release per liter of O2 during metabolism varies by substrate:

  • Fat: 19.8 kJ

  • Carbohydrate: 21.1 kJ

  • Protein: 18.7 kJ

• Basal Metabolic Rate (BMR):

  • Energy consumption at rest, varies with age and body mass.

  • Average:

  • Females: 1.1 W/kg

  • Males: 1.2 W/kg

• Implications for elderly feeling more cold due to lower BMR.

Efficiency and Energy Transfer

• Efficiency Calculation Examples:

  • Example with cyclist: ext{Efficiency} = rac{2400 kJ}{10000 kJ} = 0.24 ext{ or } 24 ext{%}.

  • The energy difference indicates energy lost as heat.

• Heat Transfer for Temperature Changes:

  • Example of 60 ext{ kg} body with a temperature rise of 0.4 °C:

  • Q = mc riangle T = (60 kg)(3470 J kg^{-1} °C^{-1})(0.4 °C) = 83 kJ, indicating limited energy retention as temperature can only absorb a small amount overall.