LR

RGI.15 - Thermodynamics and the Human Body

Thermodynamics

  • The study of the relationship between thermal and mechanical energy.

First Law of Thermodynamics

  • States that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
  • U{final} - U{initial} = Q - W
    • Q = amount of heat energy added to or taken out of the system.
      • Q > 0: Heat added to the system (Q is +).
      • Q < 0: Heat removed from the system (Q is -).
    • W = the amount of work done to or by the system.
    • U = internal energy of a system.
  • Restatement of the law of conservation of energy.
  • You can't get more energy out of a system than you put in.
  • YOU CAN’T WIN or There’s no such thing as a free lunch.

Kinetic Energy of a Gas Molecule

  • The average kinetic energy for a gas molecule is given by:
    • KE = (3/2) * k_B * T
      • T = Temperature (K).
      • k_B = Boltzmann Constant = 1.38 x 10^{-23} JK^{-1}.
  • For a gas system of N molecules, the total energy in the system is:
    • Total Energy = (3/2) * N * k_B * T
  • The amount of energy in a system depends on the temperature.

Second Law of Thermodynamics

  • States that we can never convert 100% of the available energy into usable work.
  • YOU CAN’T BREAK EVEN!
  • The process of converting heat energy into mechanical energy is always inefficient.
  • Some of the previously available energy becomes permanently unavailable.
  • Everything in the universe eventually moves from order to disorder, and entropy is the measurement of that change.
  • Entropy: A thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.
  • Irreversibility of natural processes, especially of temperature.

Efficiency

  • Efficiency (\epsilon) of a system is defined as:
    • \epsilon = Work Done / Energy Supplied
  • \epsilon is always less than 1.
  • Examples of efficiency in different activities:
    • Shovelling: 3%
    • Weight Lifting: 9%
    • Turning Heavy Wheel: 13%
    • Climbing Ladder: 19%
    • Climbing Stairs: 23%
    • Cycling: 25%
    • Walking up 5-degree slope: 30%

The Human Body as an Engine

  • The fuel that the human body runs on is O2 and Food.
  • The usual unit of energy used in the life-sciences is the kilocalorie (kcal), which is mis-termed the calorie (cal) by dieticians.
    • 1 kcal = 4.2 kJ
    • 1 kJ = 0.24 kcal
  • Energy Content: The ratio of the energy released to the mass of foodstuff consumed.
  • Energy Equivalent of O2: The ratio of the energy released to the volume of O2 consumed.
  • Energy is extracted from food via oxidation.
    • C6H{12}O6 + 6O2 \rightarrow 6CO2 + 6H2O + 2870kJ (686 kcal)
      • (180g) (134.4 L)

Oxidation of Glucose

  • C6H{12}O6 + 6O2 \rightarrow 6CO2 + 6H2O + 2870 kJ (686 kcal)
    • (180 g) (134.4 litres)
  • Energy content = 686 kcal / 180 g = 3.8 kcal / g
  • Energy equivalent = 686 kcal / 134.4 L = 5.1 kcal / litre

Energy Content and Energy Equivalent of Different Food Types

  • Carbohydrate:
    • Energy Content: 4 kcal/g
    • Energy Equivalent O2: 5.047 kcal/L
  • Protein:
    • Energy Content: 4 kcal/g
    • Energy Equivalent O2: 4.485 kcal/L
  • Fat:
    • Energy Content: 9 kcal/g
    • Energy Equivalent O2: 4.686 kcal/L

Fat Stores and Protein Metabolism

  • If fat stores are completely depleted, the body starts to metabolise protein as the next available source.
  • Muscle mass begins to diminish, a classic symptom of malnutrition.

Metabolic Rate

  • Energy Content varies widely with food-type, but the Energy Equivalent of O2 is fairly constant for all types of food.
  • Measuring O2 consumption rate is a good way of determining the rate of energy consumption in the body - the Metabolic Rate.
  • Metabolic rate is usually at a minimum while we sleep (slow breathing rate).
  • During exercise, we require lots of energy (high metabolic rate), need to oxidize lots of foodstuffs (very fast breathing).

Oxygen Consumption

  • Average lung capacity is about 5-6 litres, but the tidal volume is typically only about 0.5 litres.
  • Only ~20% of this is O2, so in one breath, we take in ~ 0.1 L of O2.
  • However, only ~22% of the inhaled O2 gets absorbed into the blood stream:
    • 0.1 \text{ litre} \times 0.22 = 0.022 \text{ L per breath}
  • At rest, we have about 11 breaths per minute, so the total amount of O2 absorbed per minute is:
    • 0.022 \text{ L} \times 11 = 0.242 \text{ litres}
  • The average energy consumption rate while awake is:
    • (0.242 \text{ L} / \text{min}) \times (5 \text{ kcal} / \text{L}) = 1.1 - 1.2 \text{ kcal} / \text{min per person}
  • Minimum daily energy requirement is therefore:
    • (1.1 \text{ to } 1.2 \text{ kcal} / \text{min}) \times 60 \text{ min} \times 24 \text{ hrs} = 1584 \text{ to } 1728 \text{ kcal per person}

Basal Metabolic Rate (BMR)

  • Even while we are asleep, the body is expending energy to keep the essential body processes operating.
  • Basal Metabolic Rate (BMR) is the rate of energy consumption while resting but awake.
  • BMR = 1.1 to 1.2 W/kg = 1500 to 1700 kcal/day for a 60-70 kg person
  • Components of daily energy expenditure:
    • Exercise Activity Thermogenesis (5%)
    • Non-Exercise Activity Thermogenesis
    • Thermic Effect of Food (10%) (the amount of energy it takes for your body to digest, absorb, and metabolise the food you eat)
    • BMR (65% - 75%)

Energy Expenditure Examples

  • Resting, Sleeping, Chemistry Lecture: 70 kcal/hr
  • Walking: 250 kcal/hr
  • Swimming, Cycling, Shivering: 450 kcal/hr
  • Jogging, Basketball: 600 kcal/hr
  • ~1 minute extreme exertion (400 m Sprint): 700 kcal/hr
  • ~10 sec extreme exertion (100 m Sprint): 1200 kcal/hr

Metabolic Rates of Mammals

  • Rate of heat loss depends on surface area.
  • Mass & density are related, so can say M depends on L3:
    • \rho = m/vol
    • m = \rho \cdot vol
  • If the rate of heat loss depends on M^{2/3}, it's reasonable to assume that the rate of heat production follows the same trend.
  • Zoological studies have shown that the relation is closer to M^{3/4}. This is known as Kleiber’s Law.

Kleiber's Law

  • Metabolic rate scales with mass to the power of 3/4 (M^{3/4}).

Scaling Example: Metabolic Rate

  • Mouse:
    • Weight: 1 oz
    • Energy consumption: 4 kcal/day (4 kcal per oz. per day)
  • Elephant:
    • Weight: 12,000 lb
    • Energy consumption: 40,000 kcal per day (0.2 kcal per lb per day)
  • The bigger the animal, the more efficiently it uses energy.
  • The average elephant weighs 220,000 times as much as the average mouse but requires only about 10,000 times as much energy in the form of food calories to sustain itself.