Question

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant- pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constantpressure process, \(\Delta H=0 .\) What can you conclude about \(\Delta E, q\) and \(w ?\)

Short answer

(a) The enthalpy change (\(\Delta H\)) is equal to the heat transfer (\(q\)) under constant pressure conditions, such as \(\Delta H = q_P\). (b) When the system releases heat to the surroundings during a constant-pressure process, the enthalpy of the system decreases (\(\Delta H < 0\)). (c) For a constant-pressure process with \(\Delta H = 0\), we can conclude that \(\Delta E = 0\), \(q = 0\), and \(w = 0\).

Step-by-step solution

a) Condition for enthalpy change equal to heat transfer

The enthalpy change (\(\Delta H\)) is equal to the heat transfer (\(q\)) under constant pressure conditions. Mathematically, this can be expressed as follows: \[\Delta H = q_P\] where \(P\) denotes constant pressure.

b) Enthalpy change during heat release in a constant-pressure process

When the system releases heat to the surroundings during a constant-pressure process, the heat transfer (\(q\)) is negative (i.e., \(q < 0\)), as energy is flowing out of the system. According to the relationship in part (a), we have \(\Delta H = q_P\), so if \(q_P < 0\), then \(\Delta H < 0\). This means that the enthalpy of the system decreases during the process.

c) Conclusion for \(\Delta H = 0\) in a constant-pressure process

When \(\Delta H = 0\) in a constant-pressure process, the heat transfer (\(q_P\)) equals zero as well, since \(\Delta H = q_P\). We can use this information and the first law of thermodynamics to determine the values or relationships of \(\Delta E\) and \(w\). The first law of thermodynamics can be expressed as: \[\Delta E = q + w\] Since \(\Delta H = 0\) and we know that \(\Delta H = q_P\), we have: \[q + w = 0\] Since \(q = 0\) (no heat transfer), the only way for the equation to be satisfied is when \(w = 0\). Therefore, for a constant-pressure process with \(\Delta H = 0\), we can conclude that \(\Delta E = 0\), \(q = 0\), and \(w = 0\).

Key concepts

Enthalpy

Enthalpy is a foundational concept in thermodynamics related to the heat of a system. It is a property that combines the system's internal energy with the work done by the system due to pressure and volume changes. Enthalpy, represented as \(H\), is defined as:\[ H = E + PV \]where \(E\) is the internal energy, \(P\) is the pressure, and \(V\) is the volume of the system. This means enthalpy is a measure of energy in the form of heat within a system under constant pressure conditions. A change in enthalpy, \(\Delta H\), is crucial during chemical reactions where heat exchange with the surroundings occurs. For instance, when a reaction takes place at constant pressure, the enthalpy change equals the heat transferred, denoted by:\[ \Delta H = q_P \]"\(q_P\)" represents the heat transferred at constant pressure. Thus, enthalpy change indicates whether a process absorbs or releases heat.

Constant-pressure process

In thermodynamics, a constant-pressure process is a process where the pressure within the system remains unchanged even as other parameters, such as temperature or volume, might vary. This is particularly relevant in many natural and industrial processes, where pressure equilibrium is maintained with the surroundings. During a constant-pressure process, the enthalpy change \((\Delta H)\) directly corresponds to the heat exchanged \((q_P)\). If heat is released to the surroundings, as with exothermic reactions, \(q_P\) is negative, indicating a decrease in enthalpy:

• \(\Delta H < 0\) – The system's enthalpy decreases when it releases heat.
• \(\Delta H > 0\) – The system's enthalpy increases if it absorbs heat.

Understanding constant-pressure processes is essential for predicting system behavior during heat exchange, especially in chemical reactions and phase changes.

First law of thermodynamics

The first law of thermodynamics is a principle of conservation of energy, stating that energy cannot be created or destroyed, only transformed or transferred. In formula terms, this is expressed as:\[ \Delta E = q + w \]where \(\Delta E\) represents a change in internal energy, \(q\) is the heat added to the system, and \(w\) is the work done by the system. In constant-pressure processes where \(\Delta H = 0\), the heat change \(q_P\) is zero, leading to:\[ q + w = 0 \]This demonstrates that, in such cases, any work done by or on the system is internally compensated by changes, keeping the internal energy \(\Delta E\) unchanged. Consequently, for a process with no net heat exchange and no work done \((w = 0)\), both \(\Delta E\) and \(q\) are zero, illustrating energy balance in thermodynamic processes.