2.1 First law of thermodynamics

The first law of thermodynamics is a fundamental principle in statistical mechanics, linking microscopic particle behavior to macroscopic energy conservation. It states that energy can't be created or destroyed, only converted between forms, providing a foundation for analyzing thermodynamic processes and energy transformations.

This law is crucial for understanding heat engines, chemical reactions, and other energy-related phenomena. It introduces key concepts like internal energy, work, and heat transfer, connecting them through mathematical formulations that bridge the gap between statistical mechanics and observable thermodynamic behavior.

Fundamental concepts

• Statistical mechanics provides a microscopic foundation for understanding macroscopic thermodynamic phenomena
• The first law of thermodynamics emerges from the statistical behavior of large numbers of particles
• Energy conservation serves as a cornerstone principle connecting microscopic and macroscopic descriptions of physical systems

Energy conservation principle

Top images from around the web for Energy conservation principle

• 

  The First Law of Thermodynamics · Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics and Some Simple Processes · Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics | Boundless Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics · Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics and Some Simple Processes · Physics View original

  Is this image relevant?

1 of 3

Top images from around the web for Energy conservation principle

• 

  The First Law of Thermodynamics · Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics and Some Simple Processes · Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics | Boundless Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics · Physics View original

  Is this image relevant?

• 

  The First Law of Thermodynamics and Some Simple Processes · Physics View original

  Is this image relevant?

1 of 3

• Fundamental law stating energy cannot be created or destroyed, only converted between forms
• Applies to isolated systems where total energy remains constant over time
• Underpins all thermodynamic processes and energy transformations
• Mathematically expressed as $\Delta E_{total} = 0$ for a closed system
• Crucial for analyzing heat engines, refrigeration cycles, and chemical reactions

System and surroundings

• System refers to the specific part of the universe under study (gas in a piston, chemical reaction)
• Surroundings encompass everything outside the system boundaries
• Three main types of systems
  • Open systems allow transfer of both energy and matter
  • Closed systems permit energy transfer but not matter
  • Isolated systems prohibit both energy and matter exchange
• Proper definition of system boundaries essential for applying first law correctly

Thermodynamic equilibrium

• State where macroscopic properties of a system remain constant over time
• Achieved when thermal, mechanical, and chemical equilibria are simultaneously satisfied
• Thermal equilibrium occurs when temperatures equalize throughout the system
• Mechanical equilibrium involves uniform pressure distribution
• Chemical equilibrium requires balanced chemical potentials for all components
• Essential concept for defining thermodynamic state variables and applying first law

Internal energy

• Internal energy represents the total energy contained within a thermodynamic system
• Closely related to the microscopic kinetic and potential energies of particles
• Forms the basis for understanding energy transformations in statistical mechanics

Definition and properties

• Sum of all microscopic forms of energy within a system
• Includes kinetic energy of molecular motion and potential energy of intermolecular forces
• Depends on the system's temperature, volume, and composition
• Cannot be directly measured, only changes in internal energy can be observed
• Represented by the symbol U in thermodynamic equations

Extensive vs intensive variables

• Internal energy classified as an extensive variable, scaling with system size
• Contrasts with intensive variables like temperature and pressure, independent of system size
• Extensive properties (U, V, S) scale linearly with amount of substance
• Intensive properties (T, P, ρ) remain constant when system is divided
• Relationship between extensive and intensive variables crucial for thermodynamic analysis

State function characteristics

• Internal energy defined as a state function, depending only on current system state
• Independent of the path taken to reach that state
• Allows calculation of energy changes between two states without knowing intermediate steps
• Enables use of convenient reference states for energy calculations
• Simplifies analysis of complex thermodynamic processes

Work in thermodynamics

• Work represents energy transfer between a system and its surroundings through macroscopic motion
• Closely related to force and displacement in classical mechanics
• Plays a crucial role in connecting statistical mechanics to observable thermodynamic phenomena

Mechanical work

• Energy transfer resulting from application of force over a distance
• Calculated as the product of force and displacement in the direction of force
• Expressed mathematically as $W = \int \vec{F} \cdot d\vec{x}$
• Sign convention defines work done by the system as positive
• Includes various forms such as gravitational, elastic, and electrical work

Pressure-volume work

• Most common form of work in thermodynamic systems
• Occurs when a system expands or contracts against an external pressure
• Calculated using the formula $W = -\int P_{ext} dV$
• Negative sign indicates work done on the system during compression
• Graphically represented as the area under a P-V curve

Other forms of work

• Electrical work involves movement of charges in an electric field
• Magnetic work results from changes in magnetic fields
• Surface tension work occurs in systems with fluid interfaces
• Chemical work associated with changes in chemical composition
• Generalized work term can be expressed as $dW = Y dX$ where Y is a generalized force and X a generalized displacement

Heat transfer

• Heat represents energy transfer between systems due to temperature differences
• Closely related to the microscopic motion of particles in statistical mechanics
• Plays a fundamental role in understanding thermal equilibrium and energy flow

Heat as energy transfer

• Process of thermal energy transfer between bodies at different temperatures
• Occurs spontaneously from higher to lower temperature regions
• Quantified by the amount of energy transferred, measured in joules (J)
• Distinct from internal energy, which is a state function
• Crucial for understanding thermal equilibration in statistical systems

Conduction vs convection vs radiation

• Conduction involves direct transfer of thermal energy through collisions between particles
  • Dominant in solids, characterized by Fourier's law of heat conduction
• Convection occurs through bulk motion of fluids
  • Natural convection driven by buoyancy forces
  • Forced convection induced by external means (fans, pumps)
• Radiation transfers energy through electromagnetic waves
  • Described by Stefan-Boltzmann law for blackbody radiation
  • Significant at high temperatures or in vacuum conditions

Sign convention for heat

• Heat absorbed by the system defined as positive
• Heat released by the system considered negative
• Consistent with work sign convention in first law of thermodynamics
• Allows for unified treatment of energy transfers in thermodynamic equations
• Essential for correctly applying the first law to various processes

Mathematical formulation

• The first law of thermodynamics can be expressed mathematically in various forms
• These equations provide a quantitative framework for analyzing energy transformations
• Crucial for connecting microscopic statistical mechanics to macroscopic thermodynamic behavior

First law equation

• Fundamental statement of energy conservation in thermodynamic systems
• Expressed as $\Delta U = Q - W$ for a closed system
• ΔU represents change in internal energy
• Q denotes heat transferred to the system
• W signifies work done by the system
• Applies to both reversible and irreversible processes

Differential form

• Instantaneous rate of change in internal energy expressed as $dU = đQ - đW$
• đQ and đW represent inexact differentials (path-dependent quantities)
• Useful for analyzing infinitesimal changes in thermodynamic variables
• Allows for integration along specific paths to determine finite changes
• Forms basis for deriving thermodynamic relations and equations of state

Integral form

• Expresses finite changes in internal energy over a process
• Written as $\Delta U = \int_{i}^{f} đQ - \int_{i}^{f} đW$
• Integrations performed along the specific path of the process
• Useful for analyzing cyclic processes where initial and final states coincide
• Enables calculation of net heat and work exchanges in thermodynamic cycles

Processes and applications

• Various thermodynamic processes can be analyzed using the first law
• These processes form the basis for understanding real-world applications
• Connecting statistical mechanics to practical engineering and scientific problems

Isothermal processes

• Temperature remains constant throughout the process
• Requires continuous heat exchange with surroundings to maintain temperature
• For ideal gases, follows the equation $PV = constant$
• Work done calculated as $W = nRT \ln(V_f/V_i)$ for ideal gases
• Applications include isothermal compression in gas storage, some biological processes

Adiabatic processes

• No heat exchange occurs between system and surroundings
• Characterized by the equation $PV^\gamma = constant$ for ideal gases
• γ represents the ratio of specific heats (Cp/Cv)
• Temperature changes as work is done on or by the system
• Examples include rapid compression in diesel engines, atmospheric processes

Isobaric vs isochoric processes

• Isobaric processes occur at constant pressure
  • Work done calculated as $W = P\Delta V$
  • Common in many chemical reactions, constant pressure calorimetry
• Isochoric processes maintain constant volume
  • No pressure-volume work done ($W = 0$)
  • Heat transfer directly increases internal energy
  • Occurs in sealed containers, bomb calorimetry experiments

Enthalpy

• Enthalpy serves as a useful thermodynamic potential for analyzing constant pressure processes
• Closely related to internal energy but incorporates the PV term
• Important concept in statistical mechanics for understanding energy changes in chemical systems

Definition and significance

• Defined as $H = U + PV$ where U is internal energy, P is pressure, and V is volume
• State function like internal energy, depends only on current system state
• Particularly useful for analyzing processes at constant pressure
• Change in enthalpy ΔH represents heat transferred at constant pressure
• Widely used in chemistry to describe heat of reaction, formation, and phase transitions

Relationship to internal energy

• Difference between enthalpy and internal energy given by PV term
• For ideal gases, $H = U + nRT$ where n is number of moles and R is gas constant
• Change in enthalpy related to change in internal energy by $\Delta H = \Delta U + \Delta(PV)$
• For constant pressure processes, $\Delta H = \Delta U + P\Delta V$
• Enthalpy changes can be measured more easily than internal energy changes in many cases

Constant pressure processes

• Enthalpy change equals heat transferred at constant pressure
• Expressed mathematically as $\Delta H = Q_p$ where Qp is heat at constant pressure
• Simplifies analysis of many chemical and physical processes
• Used to define standard enthalpies of formation, reaction, and phase change
• Important for understanding energy changes in atmospheric processes, chemical engineering

Specific heats

• Specific heats quantify the amount of heat required to raise the temperature of a substance
• Closely related to the microscopic degrees of freedom in statistical mechanics
• Essential for understanding thermal properties and energy storage in materials

Heat capacity at constant volume

• Defined as $C_v = (\partial U / \partial T)_V$
• Measures energy required to raise temperature with volume held constant
• Related to internal energy changes in isochoric processes
• For ideal monatomic gases, $C_v = (3/2)R$ per mole
• Lower than Cp due to no work done against external pressure

Heat capacity at constant pressure

• Expressed as $C_p = (\partial H / \partial T)_P$
• Quantifies heat needed to raise temperature at constant pressure
• Includes both internal energy increase and work done against atmosphere
• For ideal gases, $C_p = C_v + R$ where R is the gas constant
• Generally larger than Cv for most substances

Relationship between specific heats

• Ratio of specific heats defined as $\gamma = C_p / C_v$
• Important parameter in adiabatic processes for ideal gases
• For monatomic ideal gases, γ = 5/3
• Diatomic gases typically have γ ≈ 7/5 at room temperature
• Relationship derived from statistical mechanics based on molecular degrees of freedom

Cyclic processes

• Cyclic processes form the basis for many heat engines and refrigeration cycles
• Understanding these cycles connects statistical mechanics to practical thermodynamic applications
• Analysis of cyclic processes reveals fundamental limits on thermal efficiency

Carnot cycle

• Ideal reversible cycle operating between two temperature reservoirs
• Consists of two isothermal and two adiabatic processes
• Maximum possible efficiency given by $\eta = 1 - T_C / T_H$
• Serves as a theoretical upper limit for all heat engines
• Crucial for understanding the second law of thermodynamics

Otto cycle

• Idealized cycle for spark-ignition internal combustion engines
• Four-stroke cycle consisting of isentropic compression, isochoric heating, isentropic expansion, and isochoric cooling
• Efficiency depends on compression ratio and specific heat ratio
• Thermal efficiency given by $\eta = 1 - (1/r^{\gamma-1})$ where r is compression ratio
• Used to analyze performance of gasoline engines

Diesel cycle

• Idealized cycle for compression-ignition engines
• Similar to Otto cycle but with isobaric combustion instead of isochoric
• Characterized by higher compression ratios than Otto cycle
• Thermal efficiency depends on compression ratio and cut-off ratio
• Generally more efficient than Otto cycle but with slower engine speeds

First law limitations

• The first law of thermodynamics, while fundamental, has certain limitations
• Understanding these limitations motivates the development of the second law
• Connects statistical mechanics to the concept of entropy and irreversibility

Reversible vs irreversible processes

• Reversible processes can be reversed without leaving any changes in the surroundings
• Irreversible processes cannot be perfectly reversed, leading to increased entropy
• Real processes are always irreversible to some degree
• First law applies to both reversible and irreversible processes
• Reversible processes achieve maximum efficiency in cyclic engines

Direction of spontaneous processes

• First law does not predict the direction of spontaneous processes
• Cannot explain why heat flows from hot to cold objects
• Fails to account for the natural tendency towards increased disorder
• Necessitates the introduction of the concept of entropy
• Second law required to predict spontaneity and equilibrium

Need for second law

• First law insufficient to fully describe real-world thermodynamic phenomena
• Second law introduces the concept of entropy and irreversibility
• Provides criteria for determining the feasibility of processes
• Establishes fundamental limits on the efficiency of heat engines
• Connects microscopic statistical behavior to macroscopic irreversibility