11.4 First law of thermodynamics

The first law of thermodynamics is a cornerstone of energy conservation in mechanical systems. It links changes in internal energy to heat transfer and work done, providing a framework for understanding energy transformations.

This law states that energy can't be created or destroyed, only converted between forms. It's expressed as ΔU = Q - W, where U is internal energy, Q is heat added, and W is work done by the system.

Definition and concept

• First law of thermodynamics establishes the fundamental principle of energy conservation in thermal systems
• Relates changes in internal energy to heat transfer and work done, forming the basis for understanding energy transformations in mechanical systems

Statement of first law

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• Energy cannot be created or destroyed, only converted from one form to another
• Total energy of an isolated system remains constant over time
• Mathematically expressed as $\Delta U = Q - W$, where U is internal energy, Q is heat added, and W is work done by the system

Conservation of energy principle

• Fundamental concept underlying the first law of thermodynamics
• Energy transfers between system and surroundings must balance
• Applies to all physical processes, including mechanical, thermal, and chemical interactions

Closed vs open systems

• Closed systems exchange energy but not matter with surroundings
• Open systems allow both energy and matter exchange
• First law applies differently to each system type, accounting for mass flow in open systems

Internal energy

Microscopic kinetic energy

• Contributes to internal energy through molecular motion
• Includes translational, rotational, and vibrational energy of particles
• Directly related to temperature, increasing as temperature rises

Microscopic potential energy

• Arises from intermolecular forces and atomic bonds
• Includes electrostatic interactions and chemical bond energies
• Changes during phase transitions and chemical reactions

Relation to temperature

• Temperature measures average kinetic energy of particles
• Higher temperature indicates greater internal energy
• Absolute zero represents minimum possible internal energy state

Work in thermodynamics

Pressure-volume work

• Most common form of work in thermodynamic systems
• Calculated as $W = \int P dV$, where P is pressure and V is volume
• Positive work done by system when expanding against external pressure

Other forms of work

• Electrical work in batteries and fuel cells
• Magnetic work in superconductors
• Surface tension work in liquid droplets
• Gravitational work in hydrostatic systems

Sign conventions

• Positive work indicates energy leaving the system
• Negative work represents energy entering the system
• Consistent sign convention crucial for accurate energy balance calculations

Heat transfer

Conduction vs convection vs radiation

• Conduction transfers heat through direct molecular collisions
• Convection involves heat transfer by fluid motion
• Radiation transmits energy via electromagnetic waves
• Each mechanism dominates in different scenarios (solids, fluids, vacuum)

Heat capacity and specific heat

• Heat capacity measures energy required to raise temperature by one degree
• Specific heat normalizes heat capacity per unit mass
• Values vary widely among materials (water has high specific heat)

Mathematical formulation

Equation for first law

• General form: $\Delta U = Q - W$
• For open systems: $\Delta U = Q - W + \sum m_i h_i - \sum m_e h_e$
• Accounts for energy flows across system boundaries

Change in internal energy

• Calculated as $\Delta U = m c_v \Delta T$ for ideal gases
• Depends on specific heat capacity at constant volume (cv)
• Independent of path taken between initial and final states

Work done on system

• Negative of work done by system: $W_{on} = -W_{by}$
• Includes all forms of work (pressure-volume, electrical, etc.)
• Path-dependent quantity, unlike internal energy change

Applications

Isochoric process

• Volume remains constant ($\Delta V = 0$)
• No pressure-volume work done
• All heat added goes into increasing internal energy

Isobaric process

• Pressure remains constant
• Work done equals $W = P \Delta V$
• Commonly encountered in constant pressure heating/cooling

Isothermal process

• Temperature remains constant ($\Delta T = 0$)
• Internal energy unchanged for ideal gases
• All heat added converted to work (or vice versa)

Adiabatic process

• No heat transfer with surroundings ($Q = 0$)
• Work done entirely at expense of internal energy
• Occurs in rapid compressions/expansions (diesel engines)

Limitations and assumptions

Ideal gas approximation

• Assumes negligible intermolecular forces
• Valid for low densities and high temperatures
• Breaks down for real gases under extreme conditions

Quasi-static processes

• Assumes system remains infinitesimally close to equilibrium
• Allows use of equilibrium thermodynamic relations
• Real processes often deviate from this idealization

Relation to other laws

Zeroth law of thermodynamics

• Establishes concept of thermal equilibrium
• Provides foundation for temperature measurement
• Complements first law in describing heat flow direction

Second law of thermodynamics

• Introduces concept of entropy and irreversibility
• Limits efficiency of heat engines and refrigerators
• Complements first law by addressing quality of energy

Experimental verification

Historical experiments

• Joule's paddle wheel experiment demonstrated mechanical equivalent of heat
• Rumford's cannon boring observations linked heat to motion
• Mayer's work on conservation of energy in biological systems

Modern laboratory techniques

• Calorimetry measures heat transfer in chemical reactions
• Bomb calorimeters determine energy content of fuels
• Differential scanning calorimetry analyzes phase transitions

Practical implications

Engineering applications

• Design of heat engines and power plants
• Optimization of refrigeration cycles
• Thermal management in electronic devices
• Energy recovery systems in industrial processes

Energy efficiency considerations

• First law efficiency measures useful output vs input energy
• Guides development of energy-saving technologies
• Informs policy decisions on energy conservation measures
• Highlights importance of waste heat recovery in industrial processes