4.1 First law of thermodynamics

The first law of thermodynamics is all about energy conservation. It's the foundation for understanding how energy moves and changes in systems, helping us figure out the relationship between heat, work, and internal energy.

This law is crucial for chemical engineers when analyzing processes. It lets us track energy flow, predict system changes, and optimize operations by balancing heat and work in various industrial applications.

First Law of Thermodynamics

Energy Conservation and the First Law

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• The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another (kinetic, potential, thermal) or transferred between systems
• This law implies that the total energy of an isolated system remains constant, as energy is conserved
• In a cyclic process, where the system returns to its initial state (Carnot cycle), the net change in internal energy is zero, and the net heat added to the system equals the net work done by the system

Closed Systems and Internal Energy Changes

• For a closed system (fixed mass), the change in internal energy ($\Delta U$) is equal to the heat added to the system ($Q$) minus the work done by the system on its surroundings ($W$): $\Delta U = Q - W$
• Positive heat ($Q > 0$) indicates energy is added to the system, while positive work ($W > 0$) indicates the system does work on its surroundings
• The first law provides a framework for analyzing energy transfer and conversion in various thermodynamic processes (isothermal, isobaric, isochoric, adiabatic)

Heat, Work, and Internal Energy

Defining Heat, Work, and Internal Energy

• Heat ($Q$) is the energy transferred between a system and its surroundings due to a temperature difference, measured in joules ($J$) or calories ($cal$)
• Work ($W$) is the energy transferred between a system and its surroundings due to a force acting through a distance, also measured in joules ($J$)
• Internal energy ($U$) is the total kinetic and potential energy of the particles within a system, a measure of the system's ability to do work or transfer heat

Relating Heat, Work, and Internal Energy

• The first law of thermodynamics relates these quantities as $\Delta U = Q - W$ for a closed system
• This equation shows that the change in internal energy of a system is equal to the net energy transfer through heat and work
• For example, in an isothermal expansion of an ideal gas, the internal energy remains constant ($\Delta U = 0$), so the heat added to the system equals the work done by the system ($Q = W$)

Applying the First Law

Problem-Solving Steps

• Identify the system and its boundaries, determining whether it is a closed system (fixed mass) or an open system (mass transfer across boundaries)
• Determine the initial and final states of the system, noting any changes in temperature, pressure, volume, or other relevant properties
• Identify the process or processes occurring within the system (isothermal, isobaric, isochoric, adiabatic)
• Apply the first law equation ($\Delta U = Q - W$) to solve for the unknown quantity (change in internal energy, heat transferred, or work done)

Additional Considerations

• Use appropriate sign conventions for heat and work, with heat added to the system and work done by the system being positive
• Consider any additional equations or relationships relevant to the specific process, such as the ideal gas law ($PV = nRT$) or equations for specific types of work (boundary work, shaft work)
• For example, in an isobaric process (constant pressure), the boundary work done by the system is given by $W = P\Delta V$, where $P$ is the constant pressure and $\Delta V$ is the change in volume

State Functions vs Path Functions

Defining State and Path Functions

• A state function is a property that depends only on the current state of the system, not on the path taken to reach that state (internal energy $U$, enthalpy $H$, entropy $S$, Gibbs free energy $G$)
• A path function is a quantity that depends on the specific path taken by the system from its initial state to its final state (heat $Q$, work $W$)

Implications for Thermodynamic Processes

• Changes in state functions ($\Delta U$, $\Delta H$, $\Delta S$) are independent of the path and can be calculated using only the initial and final states of the system
• Path functions ($Q$ and $W$) cannot be determined solely from the initial and final states; they require knowledge of the specific process or path followed by the system
• For a cyclic process, the net change in any state function is zero, as the system returns to its initial state (heat engines). However, the net heat and work may be non-zero, as they depend on the path