δh = δu + pδv

Definition

The equation $$ ext{δh} = ext{δu} + p ext{δv}$$ describes the relationship between changes in enthalpy (h), internal energy (u), pressure (p), and volume (v) in a thermodynamic process. This equation highlights how enthalpy change depends on the internal energy change and the work done due to volume change against pressure. Understanding this relationship is crucial when analyzing systems where pressure-volume work is significant, particularly in processes that have path-dependent characteristics.

5 Must Know Facts For Your Next Test

1. The equation shows that enthalpy change accounts for both internal energy change and the work associated with volume changes against external pressure.
2. This relationship is particularly useful for understanding reactions and phase changes that occur at constant pressure, such as in calorimetry.
3. In an ideal gas, this equation simplifies since changes in internal energy are directly related to temperature changes, making it easier to analyze thermodynamic processes.
4. The term $$p ext{δv}$$ represents the work done by or on the system as it expands or contracts, emphasizing the significance of pressure in determining enthalpy changes.
5. In practical applications, understanding this equation helps predict how energy will be transferred in systems involving chemical reactions or phase transitions under varying pressures.

Review Questions

• How does the equation $$ ext{δh} = ext{δu} + p ext{δv}$$ illustrate the concept of path dependence in thermodynamics?
  • The equation $$ ext{δh} = ext{δu} + p ext{δv}$$ illustrates path dependence because the changes in enthalpy (δh) can vary based on how a system moves from its initial to final state. The path taken can affect the values of internal energy change (δu) and work done (pδv) due to variations in pressure and volume during that process. Different paths may involve different amounts of work done, leading to different enthalpy changes even if the initial and final states are identical.
• Discuss how the components of the equation $$ ext{δh} = ext{δu} + p ext{δv}$$ relate to processes occurring at constant pressure.
  • In processes at constant pressure, the equation $$ ext{δh} = ext{δu} + p ext{δv}$$ becomes particularly relevant because enthalpy change (δh) directly reflects heat transfer to or from the system. Since pressure remains constant, any work done related to volume change is easily calculated as $$p ext{δv}$$. This makes it clear that at constant pressure, the heat absorbed or released by the system is equal to the change in enthalpy, which simplifies many calculations in thermodynamics.
• Evaluate how understanding $$ ext{δh} = ext{δu} + p ext{δv}$$ can influence real-world applications such as chemical engineering or environmental science.
  • Understanding $$ ext{δh} = ext{δu} + p ext{δv}$$ is crucial for chemical engineering and environmental science because it provides insights into energy transfer during reactions or phase changes under varying conditions. For instance, engineers can predict how different pressures will impact reaction enthalpies, optimizing conditions for maximum yield. In environmental science, recognizing how enthalpy changes affect atmospheric processes can inform climate modeling. This knowledge also aids in designing efficient systems for energy conversion, storage, and management, highlighting its importance across various real-world applications.

Related terms

Enthalpy: A thermodynamic quantity equivalent to the internal energy of a system plus the product of its pressure and volume, often used in processes at constant pressure.

Internal Energy: The total energy contained within a system, including kinetic and potential energy at the microscopic level.

Path Dependence: A concept that indicates the value of certain thermodynamic properties depends on the specific path taken during a process rather than just the initial and final states.