Thermodynamics and the Human Body

Thermodynamics, Work, Energy, and the Human Body

Learning Outcomes

• Understand thermal energy, heat, and mechanical equivalent of heat.
• Explain and apply specific heat capacity, latent heat, heat of fusion, and vaporization.
• Describe and quantify heat transfer by conduction, convection, radiation, and evaporative cooling.
• Understand the 1st Law of Thermodynamics.
• Understand heat & energy flows in the human body.
• Describe Metabolic & Basal Metabolic Rate (BMR) and how metabolic rate relates to oxygen consumption.

Energy and Human Life

• Human body uses chemical energy from carbohydrates, fats, etc.
• ATP is the body's "energy currency."
• Metabolism converts chemical energy into heat and chemical waste (carbon dioxide, water).
• Energy balance: $\Delta U = E<em>{in} - Q</em>{out} - W$ where $\Delta U$ is the change in internal energy, $E<em>{in}$ is energy input, $Q</em>{out}$ is heat output, and $W$ is work done.

Mechanical Equivalent of Heat

• 18th-century view: heat as a fluid called caloric.
• 19th-century experiments by James Prescott Joule showed heat represents energy transfer.
• $4.186 J$ of work is equivalent to 1 calorie (1 cal).
• $1 kcal \equiv$ Calorie (used for energy value of food).
• In the USA, 'k' and capital 'C' are often omitted.
• Australian foods mainly use Joules (J).
• 1 cal = amount of heat needed to raise the temperature of 1g of water by 1 Celsius degree.

Thermal Energy and Heat

• Internal energy includes chemical and thermal energy.
• Thermal energy is the kinetic and potential energy of atoms and molecules (translational, rotational, and vibrational).
• Heat is energy transferred due to a temperature difference.
• Q is the symbol for heat.

Mechanical Equivalent of Heat - Example

• Consuming 500 kcal of ice cream and cake, equivalent work climbing stairs (mass = 60 kg):
  • $500 kcal * 4.186 x 10^3 J/kcal = 2.1 x 10^6 J$
  • Work done climbing height h: $W = m g h$
  • $h = W/mg = (2.1 x 10^6 J) / (60 kg * 9.8 m/s^2) = 3600 m$
  • (Ignores metabolic efficiency)

Heat and Specific Heat

• Heat energy Q required to change the temperature of matter is proportional to its mass m and temperature change $\Delta T$: $Q = mc\Delta T$
• Specific heat (c) is a material property (J kg-1 K-1).
• Water has a high specific heat.
• Specific heat values for different substances:
  • Copper: 390
  • Water: 4186
  • Human body (average): 3470
  • Protein: 1700
  • Glass: 840

Phase Change and Latent Heat

• Energy is required for phase change without temperature change.
• About 540 kcal (2260 kJ) is needed to change 1 kg of water to steam.
• $Q = mc\Delta T$

Latent Heat

• Latent heat of fusion (LF): heat to change 1.0 kg of solid to liquid at melting point.
• Latent heat of vaporization (LV): heat to change 1.0 kg of liquid to vapor at boiling point.
• $Q = m L$
• For water:
  • $L_F = 333 kJ/kg$
  • $L_V = 2260 kJ/kg$
• Heat to evaporate sweat at body temperature » 2420 kJ/kg.
• Latent heat of vaporization is the major energy portion to evaporate liquid from a temperature below boiling point.

Heat Transfer: Conduction

• Heat conduction occurs through molecular collisions (requires temperature difference).
• Heat flow per unit time: $\frac{\Delta Q}{\Delta t} = kA \frac{T<em>1 - T</em>2}{l}$
• k is thermal conductivity (Wm-1K-1).
• Good thermal conductors have large k.

Thermal Conductivity Values

• Still air: 0.023
• Human tissue (excluding blood): ~0.2
• Water: ~0.6
• Aluminum: 205-240
• Copper: 384-400
• Carbon nanotube: 3500
• Diamond (natural): 2200
• Diamond (pure): 41,000
• Metals have higher thermal conductivity.

Heat Transfer - Convection

• Convection: heat flows by mass movement of molecules.
• Natural convection: due to lower density of hotter fluids.
• Convection can be natural or forced.
• In the human body, blood acts as a convective fluid (conduction is inefficient).
• Body temperature regulated by blood flow near skin surface.
• Heat is released through convection, evaporation, and radiation.

Heat Transfer - Thermal Radiation

• All matter emits thermal radiation (black body radiation) as electromagnetic waves.
• Emission rate: $\frac{\Delta Q}{\Delta t} = e\sigma A T^4$
  • $\sigma = 5.67 \times 10^{-8} Wm^{-2}K^{-4}$ (Stefan-Boltzmann constant)
  • Emissivity (e) is between 0 and 1.
  • Black objects: e » 1, shiny surfaces: e » 0.

Thermal Radiation - Emission & Absorption

• Objects absorb thermal radiation from surroundings.
• Absorption rate uses Stefan-Boltzmann Equation with the temperature of the radiative source.

Thermal Radiation and Temperature

• Wien's Law:
  • $\lambda_p = \frac{0.0029}{T}$
  • $\lambda_p$ = wavelength at peak intensity (meters).
  • T = absolute temperature (Kelvin).

Wien’s Law Example

• Skin at 37°C = 310 K, the peak emission:
  • $\lambda_p = (0.0029 m K) / (310 K) = 9 x 10^{-6} m = 9 \mu m$
  • in the infrared region.

Thermal Radiation - Thermography

• Thermography: medical imaging sensing thermal radiation.
• Warmer areas: tumors or infection; cooler areas: poor circulation.

Law of Conservation of Energy

• Total energy is neither created nor destroyed.
• Energy transforms between forms, transfers between objects, but remains constant.
• $E<em>{total} = KE + PE</em>{grav} + E<em>{heat} + E</em>{sound} + E<em>{chem} + E</em>{elec} +…$

First Law of Thermodynamics

• Work and heat change system's internal energy.
• Heat = energy transfer due to temperature difference.
• Work = energy transfer not due to temperature difference.
• First Law: $\Delta U = Q_{in} - W$

First Law of Thermodynamics

• Humans do work (walk, run, lift heavy object) that requires energy.
• Energy is also required for growth of new cells in our body.
• Metabolism: energy transformation processes within an organism.
• $\Delta U = Q_{in} - W$
  • W is work done by the body (uses energy).
  • Internal energy $\Delta U$ is not maintained by heat flow $Q_{in}$ into the body.
  • Internal energy is provided by chemical potential energy stored in food.

First Law of Thermodynamics for the Body

• $\Delta U = Q - W + E<em>{in} = E</em>{in} - Q_{out} - W$
  • $E_{in}$ = energy into system as food (fuel, biochemical).
  • $Q_{out}$ and W are outputs.
• Example: Over 8 hours, a person’s food energy intake is 10,000 kJ, 1,500 kJ of physical work is done, and 8,000 kJ is dissipated as heat. What is the change of internal energy?
  • $\Delta U = 10000 kJ – 8000 kJ – 1500 kJ = +500 kJ$

Energy Flows to and from the Body

• Overall, intake & outputs roughly balance.
• If metabolic rate exceeds work & heat loss then body temperature rises.

Metabolic Rate & Oxygen Consumption

• Approximately 20.2 kJ of energy is released per liter of $O_2$ in metabolism.
  • Fat 19.8 kJ
  • Carbohydrate 21.1 kJ
  • Protein 18.7 kJ
• $C<em>6H</em>{12}O<em>6 + 6O</em>2 \rightarrow 6CO<em>2 + 6H</em>2O + energy$ (Glucose + Oxygen -> Carbon Dioxide + Water + Energy)
• $O<em>2$ consumption measures metabolic rate. “\VO2 max measurement”
• Oxygen consumption is proportional to cardiac output (blood flow from heart).

Human Body Temperature Regulation

• Homeostasis = normal body temperature (35.6°C-37.8°C)
• Core body temperature kept at ~36.8 °C

Increased Body Temperature

• Stimulus: Increased body temperature (e.g., when exercising or the climate is hot)
• Blood warmer than hypothalamic set point in hypothalamus
• Activates heat-loss center (hypothalamus)
  • Skin blood vessels dilate: capillaries become flushed with warm blood; heat radiates from skin surface
  • Sweat glands activated: secrete perspiration, which is vaporized by body heat, helping to cool the body
• Body temperature decreases: blood temperature declines and hypothalamus heat-loss center