The change in internal energy, represented by the symbol \(\Delta E\) (or sometimes \(\Delta U\)), is a concept within thermodynamics. It quantifies the total transfer of energy that occurs when a system undergoes any physical or chemical process. Calculating this value is essential for understanding how energy is conserved and transformed. This measurement allows for a precise accounting of energy flow, which is necessary in fields like engineering and chemistry.
What Internal Energy Change Represents
Internal energy is the total energy contained within a thermodynamic system. This energy encompasses both the kinetic energy of the particles (translational, rotational, and vibrational motion) and their potential energy (chemical bond energy and intermolecular forces). A thermodynamic system is the specific part of the universe being studied, separated from its surroundings. The surroundings are everything outside the defined system with which it can exchange energy.
The \(\Delta E\) value represents the difference between the final and initial internal energy of the system. Since it depends only on these two states, it is known as a state function, meaning the path taken does not affect the calculation. A positive \(\Delta E\) indicates the system gained energy from the surroundings, while a negative \(\Delta E\) means the system lost energy.
The Two Variables: Heat and Work
Energy transfer between a system and its surroundings occurs through two measurable variables: heat (\(q\)) and work (\(w\)). Heat (\(q\)) is the transfer of thermal energy due to a temperature difference between the system and its surroundings. For example, when an ice cube melts, heat flows from the warmer surroundings to the colder system.
Work (\(w\)) is the energy transferred when a force acts over a distance, often as mechanical work. The most common type is pressure-volume (\(P-V\)) work, such as the expansion or compression of a gas.
The sign convention must be applied consistently. Energy entering the system is positive, including heat absorbed (\(q > 0\)) or work done on the system (\(w > 0\)).
Conversely, energy leaving the system is negative. This includes heat released (\(q < 0[/latex]) or work done by the system ([latex]w < 0[/latex]). Both heat and work are measured in Joules (J) or kilojoules (kJ), and [latex]\Delta E[/latex] must be expressed in the same energy unit.
Applying the First Law of Thermodynamics
The calculation of [latex]\Delta E\) is governed by the First Law of Thermodynamics, which is the law of conservation of energy. This law states that energy cannot be created or destroyed, only converted from one form to another. Mathematically, the relationship is expressed as: \(\Delta E = q + w\).
To calculate \(\Delta E\), first define the system and surroundings, then determine the values for \(q\) and \(w\) while applying the correct sign convention.
Example 1: Energy Loss
Consider a reaction that releases 500 J of heat and performs 200 J of work by expanding a piston. Since both are energy leaving the system, \(q = -500 \text{ J}\) and \(w = -200 \text{ J}\).
The total change is calculated by summing the values: \(\Delta E = (-500 \text{ J}) + (-200 \text{ J}) = -700 \text{ J}\). The negative result confirms a net loss of 700 J of energy from the system.
Example 2: Energy Gain
Contrast this with a gas compressed by the surroundings, which does 150 J of work on the system (\(w = +150 \text{ J}\)), and simultaneously absorbs 50 J of heat (\(q = +50 \text{ J}\)).
Both forms of energy transfer are positive because they add energy to the system. The calculation is \(\Delta E = (+50 \text{ J}) + (+150 \text{ J}) = +200 \text{ J}\), indicating a net gain of 200 J of internal energy.
Example 3: Mixed Transfer
A third case involves a system absorbing 1000 J of heat (\(q = +1000 \text{ J}\)) while performing 300 J of work by the system (\(w = -300 \text{ J}\)).
The calculation becomes \(\Delta E = (+1000 \text{ J}) + (-300 \text{ J}) = +700 \text{ J}\). The gain in energy from heat absorption outweighs the loss from work performed, resulting in a net increase in internal energy.
Interpreting Results in Chemical Systems
The final calculated value of \(\Delta E\) measures the energy change associated with a process. A positive \(\Delta E\) signifies that the system accumulated energy, characteristic of an endothermic process where energy is drawn from the surroundings. Conversely, a negative \(\Delta E\) indicates that the system released energy, defining an exothermic process.
Chemical processes are often studied under constant atmospheric pressure. In this scenario, scientists frequently use the related property called enthalpy change (\(\Delta H\)). Enthalpy accounts for the internal energy change plus the pressure-volume work done against the constant external pressure, summarized by the relationship \(\Delta H = \Delta E + P\Delta V\).
For reactions involving only solids or liquids, the volume change (\(\Delta V\)) is negligible, making the \(P\Delta V\) term near zero. In these cases, \(\Delta E\) is practically equal to \(\Delta H\). The calculated \(\Delta E\) value characterizes the energetic requirements or outputs of any thermodynamic process, providing a complete energy balance.