05 - Thermodynamics

TARGET DECK: MED::I::Medical Physics::05 - Thermodynamics

Thermodynamics

Enrico Giampieri – DIMES

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Temperature and Heat

Thermometric Scales – Zeroth Principle

Temperature is measured by thermometers. The main scales are:

Scale	Reference Point	Conversion
Celsius (°C)	Water triple point = 0.01°C	$T(°C)=T(K)-273.15$
Kelvin (K)	Water triple point = 273.16 K	$T(K)=T(°C)+273.15$
Fahrenheit (°F)	—	$°F=°C\times 1.8+32$

Zeroth Principle of Thermodynamics

If two objects at different temperatures are placed in thermal contact, they will reach the same temperature → thermal equilibrium. If two objects are, separately, in thermal equilibrium with a third object, then they are also in thermal equilibrium with each other.

What does the Zeroth Principle of Thermodynamics state?

If two objects are each in thermal equilibrium with a third object, they are in thermal equilibrium with each other.

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The Fahrenheit conversion formula is: $°F=$ {1:$°C\times 1.8+32$}

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Thermal Expansion of Materials

If an object has linear size $L_0$ at room temperature and is warmed by $\Delta T$:

$L=L_0(1+\alpha \Delta T)$

• $\alpha$ = thermal expansion coefficient (property of the material; dimensionless, expressed as fraction of length gained per degree)
• Expansion occurs in all dimensions → volume also changes

Note $\alpha$ is a pure number representing the fractional length gain per degree of temperature.

What is the formula for linear thermal expansion?

$L=L_0(1+\alpha \Delta T)$, where $\alpha$ is the thermal expansion coefficient of the material.

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The Limit Temperature of 0 K

For gases, a similar law applies to pressure:

$P=P_0(1+\alpha t)$

• By extrapolation, both pressure and volume approach zero at $-273.15°C$
• This was the original motivation for the Kelvin scale
• There is a deeper physical meaning: it relates to the energy of molecules

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By extrapolation, gas pressure and volume become zero at {1:$-273.15°C$}, which is absolute zero.

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Anomalous Behavior of Water at 4°C

Water Anomaly

Water reaches its maximum density at 4°C. Below this temperature, density decreases again. This is what keeps life possible in freezing temperatures: only the surface of water freezes, while the bottom remains at a stable temperature.

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Temperature and Energy

Internal Energy

Bodies have an internal (atomic) structure: their constituents move and interact through conservative forces.

• Total kinetic energy: sum of all individual kinetic energies
• Total potential energy: due to all pairwise interactions between particles
• Internal energy $U$ = total kinetic + total potential energy of all constituents

Temperature is a macroscopic quantity that measures the microscopic property called internal energy.

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Internal Energy and Temperature

Key Distinction

• Temperature: macroscopic quantity measuring only the average kinetic energy of the system
• Internal energy: sum of all kinetic and potential energies of all $N$ molecules

The larger vessel has greater total kinetic energy than a smaller one, even if the smaller one is at a higher temperature (higher average kinetic energy).

$U={\sum }_{i=0}^N(E_{C_i}+E_{P_i})$

where $E_{C_i}$ and $E_{P_i}$ are kinetic and potential energies of molecule $i$. $U$ is measured in Joules (S.I.).

For an ideal gas, internal energy takes a simple linear form:

$U=n{c}_{V}T$

where $n$ = number of particles, $c_V$ = specific heat at constant volume, $T$ = temperature.

What is internal energy?

The sum of all kinetic and potential energies of the N molecules constituting the system: $U={\sum }_{i=0}^N(E_{C_i}+E_{P_i})$

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For an ideal gas, internal energy is $U=$ {1:$n{c}_{V}T$}, which depends linearly on temperature.

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Joule’s Experiment: Heat-Work Equivalence

• Work can produce heat and vice versa
• Calorie (cal): amount of heat raising the temperature of 1 g of water from 14.5°C to 15.5°C
• Kilocalorie (kcal or Cal): amount of heat raising the temperature of 1 kg of water by 1°C

$1\text{ J}=0.238\text{ cal}$

What is the mechanical equivalent of the calorie?

$1\text{ J}=0.238\text{ cal}$

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Human Metabolism

• Humans and animals perform work: movements, including cellular and sub-cellular work (e.g., active transport)
• Internal energy loss from the body is mainly due to outward heat flow
• Living organisms are open systems: both energy and matter can flow in and out
• Food → biochemical transformations → internal energy → heat or mechanical work

Metabolism The set of biochemical reactions that transform energy in an organism is called metabolism.

• Metabolic rate: rate of internal energy transformation (kcal/h or Watts)
• Adult human at rest: ~70 W; normal activity: ~460 W
• ~35% of food energy is stored as ATP molecules
• Due to energy dissipation, only ~27% reaches cells

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An adult human consumes approximately {1:70 W} at rest and {2:460 W} during normal activity.

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Approximately {1:35%} of food energy is stored as ATP, and only {2:27%} reaches the cells.

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Heat Transfer

Heat Capacity and Specific Heat

For a body at temperature $T$ that absorbs heat $Q$ and changes temperature by $\Delta T$:

Heat capacity: $C=\frac{Q}{\Delta T}[\text{J}\cdot °C^{-1}]$

Specific heat (heat capacity per unit mass): $c=\frac{C}{m}=\frac{Q}{m\Delta T}[\text{J}/\text{kg}\cdot °C]$

Key difference

• $C$ (thermal capacity) depends on mass
• $c$ (specific heat) depends only on the substance

Specific heat of water: $c_{H_{2}O}=4186\text{ J/kg}°C=1000\text{ cal/kg}°C$

What is the difference between heat capacity and specific heat?

Heat capacity $C=Q/\Delta T$ depends on mass; specific heat $c=C/m$ depends only on the substance of which the body is made.

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Heat Transfer Mechanisms

Mechanism	Medium	Equation
Conduction	Solid bodies in contact	$\frac{dQ}{dt}=-KA\frac{dT}{dx}$
Convection	Fluids	$\frac{dQ}{dt}=K_{C}S(T_C-T_F)$
Irradiation	No contact required	$R=\alpha R_B=\alpha \sigma T^4$

Biological Relevance

Skin dissipates heat through irradiation, conduction, convection, and evaporation (sweating), as well as vasoconstriction and vasodilation.

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Heat Exchange Between Two Bodies

Two bodies at $T_1$ and $T_2$ in thermal contact reach equilibrium temperature $T_f$:

$m_1{c}_{V_1}(T_1-T_f)=-m_2{c}_{V_2}(T_2-T_f)$

$\Delta Q_{12}=-\Delta Q_{21}$

The warmest body gives heat to the coldest, but also vice versa with different fluxes, until equilibrium is reached.

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Heat Conduction

$\frac{dQ}{dt}=-KA\frac{dT}{dx}$

• $K$ = thermal conductivity $[\text{W}/(\text{m}\cdot °C)]$
• $A$ = cross-sectional area
• $dT/dx$ = temperature gradient
• Power measured in Watts (J/s)

Good heat conductors are usually also good electrical conductors.

Thermal Conductivity Values

Material	$K$ $[\text{W/(mcdotpK)}]$
Water	0.6
Blood	0.5
Skin	0.3
Fat	0.2
Air	0.026

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Multiple Materials and Surfaces

Heat conductivity of a surface: $C=K\cdot A$

Configuration	Formula
Parallel (side by side)	$C_{tot}=C_1+C_2$
Series (layered)	$\frac{1}{C_{tot}}=\frac{1}{C_1}+\frac{1}{C_2}$

Mnemonic – Series vs Parallel Think of thermal resistance like electrical resistance: series layers add their resistances (reciprocal of conductivity), parallel surfaces add their conductivities.

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Convection

$\frac{dQ}{dt}=K_{C}S(T_C-T_F)$

• $K_C$ = convection coefficient $[\text{W}/({\text{m}}^2\cdot °C)]$
• $S$ = surface area
• $T_C-T_F$ = temperature difference between body and fluid

Type	Mechanism
Natural	Fluid moves due to density changes with temperature
Forced	Fluid motion caused by a pump or fan

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Irradiation: Electromagnetic Waves and Photons

$E=h\nu$

• Heat transmitted via emission and absorption of electromagnetic waves
• Wavelength depends on body temperature:
  • $T<500°C$ → infrared
  • Higher $T$ → visible light

Emissive power $R$: radiant energy emitted per unit time per unit surface area

• At $T=2177°C$: $R_W\approx 500{\text{ kW/m}}^2$

When radiation hits a body, it is partly:

• Absorbed (fraction $\alpha$ = absorbing power)
• Transmitted
• Reflected

Black body An ideal body with absorbing power $\alpha =1$ (${\alpha }_B=1$). Real bodies: e.g., at 2477°C, ${\alpha }_W\approx 0.25$.

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Stefan-Boltzmann Law

$R_B=\sigma T^4$

• Emissive power of a black body depends on $T^4$
• Real body (Kirchhoff’s law): $R=\alpha R_B$

What is the Stefan-Boltzmann law?

$R_B=\sigma T^4$: the emissive power of a black body is proportional to the fourth power of its absolute temperature.

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By Kirchhoff’s law, the emissive power of a real body is $R=$ {1:$\alpha R_B$}, where $\alpha$ is its absorbing power.

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Planck’s Law: Photon Energy Distribution

Energy per unit time and unit surface in wavelength interval $[\lambda ,,\lambda +d\lambda ]$:

$E_{\lambda },d\lambda =\frac{A}{{\lambda }^5(e^{B/\lambda T}-1)},d\lambda$

where:

• $A=3.74\times 10^{-16}{\text{ W/m}}^2$
• $B=1.44\times 10^{-2}\text{ mcdotpK}$

Wien’s displacement law (peak wavelength):

${\lambda }_{max}=\frac{C}{T},C=2.8\times 10^{-3}\text{ mcdotpK}$

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According to Wien’s law, the peak wavelength of black body radiation is ${\lambda }_{max}=$ {1:$C/T$}, where $C=2.8\times 10^{-3}$ m·K.

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Thermal Exchanges in Living Organisms

Type	Description
Heterotherms	Cannot maintain constant body temperature; rely on external heat sources (e.g., sun)
Homeotherms	Warm-blooded (e.g., mammals); regulate temperature via basal metabolism

Thermoregulation occurs by varying:

1. Heat production inside the body
2. Heat exchange with the external environment (body surface)

Blood Perfusion Allows nutrient exchange and reduces thermal differences among body districts.

Heat dissipation mechanisms:

Condition	Mechanism
Hot environment	Sweating (evaporation) increases dissipation
Cold environment	Vasoconstriction reduces surface blood flow and heat exchange
Wet environment	Impairs thermoregulation: reduces sweating when hot, increases skin conductivity when cold

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Temperature and Irradiation (Biological Applications)

Thermography

• Electromagnetic radiation emitted by objects is indicative of temperature
• At room temperature, emission is mainly infrared
• Some predators (e.g., pit vipers, some reptiles) have infrared-sensitive organs to detect warm prey
• Thermograms (infrared camera images) are used in medicine
• Areas at higher temperature than surroundings may indicate malignant tumors (increased metabolic activity)
• Can also highlight vasoconstriction abnormalities, causing temperature decreases up to 28°C

Biological Temperature Sensors

• Thermoreceptors: receptor-level sensors
• Heat Shock Proteins (HSPs): recognize degraded proteins at subcellular level
• Antifreeze proteins: protect organisms at low temperatures (e.g., some Antarctic fish species)

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First Principle

Thermodynamic System

A system described through thermodynamic quantities: Pressure, Temperature, physical and chemical potentials, etc.

System Type	Energy Exchange	Matter Exchange
Isolated	✗	✗
Closed	✓	✗
Open	✓	✓

Living organisms are open thermodynamic systems (air, water, food, heat exchange) and can be analyzed through a thermodynamic approach.

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Thermodynamic Transforms

Transform	Constant Variable
Isothermal	Temperature ($T$)
Isochoric	Volume ($V$)
Isobaric	Pressure ($P$)
Adiabatic	No heat exchange with environment

Changes of thermodynamic state (phase transitions):

Transition	Direction
Fusion	Solid → Liquid
Liquefaction	Gas → Liquid
Evaporation	Liquid → Gas
Sublimation	Solid → Gas

Reversibility	Definition
Reversible	Can be retraced in both directions (e.g., heating and cooling back to initial state)
Irreversible	Occur only in one direction (e.g., mixing, spontaneous heat transfer)

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Ideal Gas

Simplest thermodynamic system: non-interacting atoms/molecules (only kinetic energy).

Work of a perfect gas (expansion/compression):

$L=P\Delta V$

Pressure definition:

$P=\frac{F}{A}[\text{Pascal}]$

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Ideal Gas State Equation

$PV=nRT$

• $n$ = number of moles
• $R=8.33\text{ J/(°Kcdotpmol)}$ = ideal gas constant

All thermodynamic transforms (isothermal, isochoric, isobaric, adiabatic) can be derived from this equation.

What is the ideal gas state equation?

$PV=nRT$, where $n$ = moles, $R=8.33\text{ J/(Kcdotpmol)}$

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First Principle of Thermodynamics

Energy Conservation $\Delta U=Q+L$

• $Q>0$: heat enters the system; $Q<0$: heat exits
• $L>0$: work performed on the system; $L<0$: work performed by the system

Heat $Q$: energy exchanged between bodies (not a state function) Work $L$: another way to change internal energy Internal energy $U$: function of state (i.e., of thermodynamic variables)

State the First Principle of Thermodynamics.

$\Delta U=Q+L$: the change in internal energy equals heat added to the system plus work done on the system. Energy is conserved.

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In the First Principle, $Q>0$ when heat {1:enters} the system, and $L<0$ when work is {2:performed by} the system.

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Enthalpy: $H=U+PV$

$H=U+P\cdot V$

• State function expressing the energy exchangeable with the environment
• For isobaric (constant $P$) transformations: $\Delta H$ = heat exchanged with the environment
• In chemical reactions where $PV$ is negligible: $\Delta H\approx \Delta U$

Sign of $\Delta H$	Reaction type
$\Delta H<0$	Exothermic
$\Delta H>0$	Endothermic

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Enthalpy is defined as $H=$ {1:$U+PV$}. A reaction with $\Delta H<0$ is {2:exothermic}.

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Hess’s Law

Since $H$ is a state function, in a complex reaction:

$\Delta H_{reaction}=H_f(\text{products})-H_f(\text{reagents})$

Methane Combustion ${\text{CH}}_4+2{\text{O}}_2\to {\text{CO}}_2+2{\text{H}}_2\text{O}$

C

From enthalpies of formation of products minus reagents: this reaction releases 891 kJ/mol.

What is Hess's Law? Since enthalpy is a state function, $\Delta H_{reaction}=H_f(\text{products})-H_f(\text{reagents})$, regardless of the reaction pathway.

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Metabolism and Body Temperature Control

ATP produced by: combustion of carbohydrates, fatty acids, and proteins.

Energy requirement: 2000–7000 kcal/day (varies by activity)

Thermogenesis balance mechanisms:

Heat Dissipation	Heat Conservation
Irradiation	Vasoconstriction
Conduction	Piloerection
Convection	Increased thermogenesis
Evaporation (sweating)	—
Vasodilation	—

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Measurement of Body Metabolism

Method	Description
Direct calorimetry	Measures heat released by body over time; hot air produced is cooled by a thermal bath and temperature is monitored
Oxygen energy equivalent	~95% of body energy from combustion; metabolic rate estimated from $\Delta [{\text{O}}_2]$ between inhaled and exhaled air

Energetic Equivalent of Oxygen In a normal diet, burning 1 L of O₂ releases approximately 4.8 kcal.

What is the energetic equivalent of oxygen?

In a normal diet, burning 1 L of oxygen releases approximately 4.8 kcal. This is used to estimate metabolic rate from oxygen consumption.

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Second Principle

Second Principle of Thermodynamics

Irreversibility

The second principle defines the irreversibility of certain thermodynamic transforms, depending on the microscopic (atomic) state of the system. It is related to thermodynamic potentials, which define the allowed direction of evolution of a system.

For a cyclic transform: $\Delta U=0\Rightarrow Q=-L$

Let $Q_H$ = absorbed heat, $Q_C$ = dissipated heat:

$Q=Q_H+Q_C=Q_H-|Q_C|=-L$

Case	Implication	Statement
$Q_H>\Vert Q_C\Vert$ → $L<0$	Thermal machine	Kelvin-Planck: impossible to convert all $Q_H$ into work
$Q_H<\Vert Q_C\Vert$ → $L>0$	Cooling machine	Clausius: impossible to transfer heat from cold to hot without work

State the Kelvin-Planck formulation of the Second Principle.

It is impossible to have a thermal machine that converts all absorbed heat $Q_H$ entirely into work (efficiency $\eta =1$ is impossible).

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Carnot Cycle and Efficiency

The Carnot cycle is the prototype of a thermal machine, consisting of two isothermal and two adiabatic transforms.

Efficiency:

$\eta =\frac{|L|}{Q_H}=\frac{Q_H-|Q_C|}{Q_H}=1-\frac{|Q_C|}{Q_H}$

Kelvin-Planck Restated It is impossible to realize a thermal machine with $\eta =1$.

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The efficiency of a Carnot thermal machine is $\eta =$ {1:$1-|Q_C|/Q_H$}, and it is impossible to achieve $\eta =$ {2:$1$}.

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Irreversibility

Hierarchy of Energy The second principle introduces the concept of irreversible transformation— absent in classical mechanics.

• Work can transform completely into heat, but not vice versa
• A hot body can provide heat to a colder one without work
• Whenever an irreversible process occurs, energy available for work diminishes

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Entropy and Irreversibility

Entropy $S$ characterizes changes in energy quality:

$\Delta S=\frac{\Delta Q}{T}$

For a system of many bodies: $d{S}_{tot}=d{S}_1+d{S}_2$

Direction of Heat Flow and Entropy When heat flows from a hot body to a cold body:

• The cold body’s entropy increases more than the hot body’s entropy decreases
• Same $Q$ exchanged (with opposite signs), but the denominator $T$ differs — larger $T$ (hot body) → smaller entropy change

$\text{In an isolated system: Entropy tends to a maximum}$

What is the thermodynamic definition of entropy change?

$\Delta S=\Delta Q/T$, where $\Delta Q$ is the heat exchanged and $T$ is the temperature of the system.

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In an isolated system, entropy {1:tends to a maximum} — it never spontaneously decreases.

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Thermodynamic Potentials

In mechanics, system evolution is governed by potential energy minimization.

In thermodynamics, the relevant potential depends on system conditions:

Potential	Symbol	Applies to
Internal energy	$U$	General
Entropy	$S$	Isolated systems
Enthalpy	$H$	Closed systems
Helmholtz free energy	$A$	—
Gibbs free energy	$G$	Open systems (const. $T$, $P$)

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Gibbs Free Energy

$G=H-TS$

where $H$ = enthalpy, $T$ = temperature, $S$ = entropy.

State function for transforms at constant $T$ and $P$; determines whether a chemical reaction occurs spontaneously.

Gibbs Free Energy Variations

$\Delta G=G(\text{products})-G(\text{reactants})$

$\Delta G$	Outcome
$\Delta G<0$	Spontaneous reaction
$\Delta G>0$	Non-spontaneous (requires additional energy, e.g., via ATP)
$\Delta G=0$	Reaction at equilibrium

Chemical reactions at constant $T$ and $P$ tend to minimize Gibbs free energy.

What does $\Delta G$ tell us about a chemical reaction?

$\Delta G<0$: spontaneous;
$\Delta G>0$: non-spontaneous (requires energy input);
$\Delta G=0$: equilibrium.

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Gibbs free energy is defined as $G=$ {1:$H-TS$}. A spontaneous reaction has $\Delta G$ {2:$<0$}.

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Spontaneous Reactions Due to Entropy

Evaporation (Sweating)

Some reactions are spontaneous even when they require energy from the environment, because they are favored by entropy.

• Evaporation in dry air: entropy-driven, takes energy away from the original system
• This is how sweating works: evaporation cools the body by drawing heat from the skin

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Biochemical Reactions: Enzymes and Catalysis

Activation Energy and Energy Barriers

In biology, biochemical reactions may need an activation energy barrier to proceed:

• Even if the total reaction is spontaneous ($\Delta G<0$), intermediate steps may require energy ($\Delta G>0$ barrier)
• These barriers serve as triggers: spontaneous reactions can have very slow kinetics without them

Enzymes Enzymes (proteins, mRNA, chemicals) act as catalysts: they lower the energy barrier, allowing the reaction to proceed. Cells regulate enzyme concentration to control the rate of biochemical reactions → control of biological processes.

What is the role of enzymes in biochemical reactions?

Enzymes act as catalysts that lower the activation energy barrier, allowing spontaneous ($\Delta G<0$) reactions to occur at a biologically useful rate.

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Enzymes {1:lower the activation energy barrier} of biochemical reactions, thereby {2:increasing their rate} without being consumed.

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Entropy: Statistical Interpretation

$S=k\cdot \log (W)$

• $W$ = number of possible microscopic configurations (microstates) for a given macroscopic state $(P,V,T)$
• $k$ = Boltzmann constant
• The system evolves toward the macroscopic state that maximizes the probability (count) of microscopic configurations

What is the statistical definition of entropy?

$S=k\cdot \log (W)$, where $W$ is the number of possible microscopic configurations (microstates) corresponding to a given macroscopic state.

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Exercises

Exercise 1: Swimming in Cold Water

Problem:

• Person slowly swimming in cold water
• Skin temperature: 35°C
• Skin surface area: 2 m²
• Water temperature: 10°C (assumed constant)
• Fat thermal conductivity: $K=0.2\text{ W/(mcdotpK)}$
• Fat tissue thickness: $\Delta x=6\text{ mm}=6\times 10^{-3}\text{ m}$

How much heat is the person losing?

Solution

Using the heat conduction equation:

$\frac{\Delta Q}{\Delta t}=\frac{K\cdot A\cdot \Delta T}{\Delta x}$

Substituting:

$\frac{\Delta Q}{\Delta t}=\frac{0.2\times 2\times (35-10)}{6\times 10^{-3}}=\frac{0.2\times 2\times 25}{0.006}=\frac{10}{0.006}\approx 1000\text{ W}=1\text{ kW}$

Result The person loses approximately 1 kW of heat to the water through conduction across the fat layer.

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Exercise 2: Meteorite in the Bathtub

Problem:

• Meteorite mass: $m_{met}=0.1\text{ kg}$, speed: $v=2000\text{ m/s}$
• Bathtub dimensions: $3\text{ m}\times 3\text{ m}\times 1\text{ m}$
• Specific heat of water: $c=600\text{ J/(kgcdotp°C)}$
• Water density: $\rho =1000{\text{ kg/m}}^3$

By how much does the water warm up?

Solution

Kinetic energy of the meteorite:

$E_k=\frac{1}{2}m{v}^2=\frac{1}{2}\times 0.1\times (2000{)}^2=200,000\text{ J}=2\times 10^5\text{ J}$

Volume of water:

$V=3\times 3\times 1=9{\text{ m}}^3$

Mass of water:

$m_{water}=\rho \cdot V=1000\times 9=9000\text{ kg}$

Temperature change:

$Q=mc\Delta T\Rightarrow \Delta T=\frac{Q}{m\cdot c}=\frac{2\times 10^5}{9000\times 600}=\frac{200,000}{5,400,000}\approx 0.037°C$

Result The water temperature rises by approximately 0.037°C — a negligible increase despite the meteorite's high speed, because the water mass is very large.

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TLDR

Thermodynamics – Complete Summary

Temperature & Scales

• Three scales: Celsius, Kelvin, Fahrenheit; Kelvin is absolute ($0\text{ K}=-273.15°C$)
• Zeroth Principle: thermal equilibrium is transitive
• Linear thermal expansion: $L=L_0(1+\alpha \Delta T)$
• Water anomaly: maximum density at 4°C → ice floats, life preserved in cold water

Internal Energy

• $U=\sum (E_{C_i}+E_{P_i})$ — sum of all kinetic + potential energies of molecules
• Temperature measures average kinetic energy; internal energy is the total
• Ideal gas: $U=n{c}_{V}T$ (linear in $T$); $PV=nRT$
• Joule equivalence: $1\text{ J}=0.238\text{ cal}$

Metabolism

• Metabolic rate: ~70 W (rest), ~460 W (activity)
• ~35% food energy → ATP; ~27% reaches cells
• Measured by direct calorimetry or O₂ consumption (1 L O₂ ≈ 4.8 kcal)

Heat Transfer

• Specific heat: $c=Q/(m\Delta T)$ — substance property
• Conduction: $dQ/dt=-KA(dT/dx)$; series/parallel combination rules
• Convection: natural (density-driven) or forced; $dQ/dt=K_{C}S(T_C-T_F)$
• Irradiation: Stefan-Boltzmann $R_B=\sigma T^4$; Planck’s law; Wien’s law ${\lambda }_{max}=C/T$
• Homeotherms: regulate via sweating (evaporation), vasoconstriction, vasodilation, piloerection
• Thermography: infrared imaging for tumor detection, vascular assessment

First Principle

• Energy conservation: $\Delta U=Q+L$
• Systems: isolated (no exchange), closed (energy only), open (energy + matter) — living organisms are open
• Enthalpy: $H=U+PV$; $\Delta H<0$ exothermic, $>0$ endothermic
• Hess’s law: $\Delta H_{rxn}=H_f(\text{products})-H_f(\text{reagents})$

Second Principle

• Defines irreversibility: work → heat completely; heat → work only partially
• Kelvin-Planck: no thermal machine has $\eta =1$; Clausius: no cooling without work
• Carnot efficiency: $\eta =1-|Q_C|/Q_H$
• Entropy: $\Delta S=\Delta Q/T$; in isolated systems $S$ tends to maximum
• Statistical interpretation: $S=k\log (W)$ — more microstates = higher entropy

Gibbs Free Energy

• $G=H-TS$; minimized at equilibrium (const. $T$, $P$)
• $\Delta G<0$: spontaneous; $\Delta G>0$: non-spontaneous; $\Delta G=0$: equilibrium
• Enzymes lower activation energy barriers → control reaction rates
• Evaporation is entropy-driven even when endothermic → basis of sweating thermoregulation