Question

For most biological processes, the changes in internal energy are approximately equal to the changes in enthalpy. Explain.

Short answer

The changes in internal energy and enthalpy are similar because pressure is constant and volume changes are small, making $P\mathrm{\Delta }V$ negligible.

Step-by-step solution

Understand Internal Energy

Internal energy, denoted as $U$, is the total energy contained within a system, including kinetic and potential energies of the molecules. It accounts for all forms of energy within the system except for the energy related to the external boundaries.

Understand Enthalpy

Enthalpy, denoted as $H$, is a thermodynamic quantity equivalent to the total heat content of a system. It is defined as $H=U+PV$, where $P$ is the pressure and $V$ is the volume. Enthalpy includes internal energy as well as the energy required to make room for it by displacing its environment.

Explain Why Changes Are Similar

In most biological processes, systems operate at constant pressure, and volume changes are relatively small compared to the internal energy changes. Mathematically, this makes the change in enthalpy $\mathrm{\Delta }H\approx \mathrm{\Delta }U+P\mathrm{\Delta }V$. Since $P\mathrm{\Delta }V$ is often negligible, $\mathrm{\Delta }H\approx \mathrm{\Delta }U$.

Summarize the Explanation

The primary reason changes in internal energy can approximate changes in enthalpy is due to the constant pressure and minimal volume changes observed in biochemical reactions. Hence, for biological processes, there's often little to no energy change associated with expansion or contraction that makes the pressure-volume work negligible.

Key concepts

Internal Energy

Internal energy is a fundamental concept in thermodynamics and is central to understanding energy changes in biological processes. It represents the total energy within a system, which includes both the kinetic energy due to the movement of molecules and the potential energy resulting from molecular interactions.
Internal energy, symbolized as $U$, plays a vital role in biochemical reactions as it accounts for all the energy that is confined within a system's boundaries. When considering biological systems, this energy can influence things like metabolic rates and cellular functions.
Although internal energy encompasses all energy forms within the system, it does not include energy cross-boundary movements, such as work done by the system or heat transferred out of the system.

• Internal energy comprises kinetic and potential energies at the molecular level.
• It is influenced by temperature, volume, and the number of particles in the system.

Understanding internal energy sets the foundation for learning about how biological processes manage and balance energy effectively.

Biological Processes

Biological processes involve various chemical reactions and physical changes that sustain life in organisms. These processes include metabolism, respiration, photosynthesis, and cellular functions.
They are often accompanied by energy transformations and changes in internal energy and enthalpy.
In biological systems, the energy required to maintain these processes comes mostly from chemical bonds within molecules.
Since most biological processes occur at a constant pressure (e.g., the constant atmospheric pressure surrounding living cells), the changes in internal energy often closely resemble changes in enthalpy.
This similarity arises because the work done in terms of pressure-volume change is frequently negligible.

• They rely over constant pressures found in living conditions.
• They contain energy transformations needing enthalpy and internal energy consideration.

By exploring biological processes, we gain more insights into how life's chemical processes operate energetically consistently.

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and energy changes in systems. It provides the framework for understanding how energy changes occur, including in biological systems.
Enthalpy and internal energy are both integral parts of thermodynamics, providing insights into reactions and processes at the cellular level.
Thermodynamics helps to determine how organisms maintain stable internal conditions, despite external changes, by explaining energy transformations.
The first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed, is particularly relevant in biological contexts.

• Describes energy exchanges in terms of heat and work.
• In biology, it relates to processes like metabolism and energy transfer.

Studying thermodynamics enables us to predict the outcomes of reactions and understand how biological systems harness energy to sustain life.

Constant Pressure

In many biological processes, reactions occur under constant pressure. This trait is vital because it simplifies the calculations related to changes in internal energy and enthalpy.
For example, consider cellular reactions that occur within compartments shielded from pressure fluctuations, like intracellular processes.
When pressure is constant, the relation between enthalpy and internal energy becomes straightforward: changes in enthalpy ($\mathrm{\Delta }H$) nearly equal changes in internal energy ($\mathrm{\Delta }U$), due to minimal work being done by pressure-volume changes.
Constant pressure environments ensure that the energy changes in these processes are more predictable and manageable.

• Pressure remains steady, simplifying energy calculations.
• Works closely with enthalpy changes due to its constancy.

This factor makes calculations for biochemical processes more straightforward, aiding in the study of energy transformations in living systems.

Negligible Volume Change

In biological systems, volume changes during chemical reactions are typically so small that they can often be ignored. This is an essential factor when comparing internal energy and enthalpy changes.
Because the work performed due to a volume change, represented by $P\mathrm{\Delta }V$, is insignificant in most biological reactions, the difference between changes in enthalpy and internal energy is minimal.
This small change ensures that $\mathrm{\Delta }H\approx \mathrm{\Delta }U$, simplifying our understanding of energy changes in biological processes.

• Volume changes are small and often negligible in biological contexts.
• Helps equate internal energy changes closely to enthalpy changes.

Understanding the impact of small volume changes helps provide clarity on why biochemical processes in living organisms often see little distinction between enthalpy and internal energy variations.