Problem 72 - A Complete Resource Book in Chemistry for JEE Main

Question

Identify the state function among the following: (a) \(\mathrm{Q}\) (b) \(\mathrm{Q}-\mathrm{w}\) (c) \(\mathrm{Q} / \mathrm{w}\) (d) \(\mathrm{Q}+\mathrm{w}\)

Step-by-Step Solution

Answer

The state function is Q-w (option b).

Step 1: Understanding State Functions

A state function is a property of a system that depends only on the current state of the system, not on the path taken to get there. This means that the value of a state function is the same no matter how the process is carried out. Examples of state functions includes properties like internal energy, enthalpy, and entropy.

Step 2: Analyzing Option (a) Q

Q represents heat, which is not a state function because the amount of heat added or removed can depend on the path taken between two states.

Step 3: Analyzing Option (b) Q-w

Q-w represents a change in internal energy (∆U), according to the first law of thermodynamics: ∆U = Q - w, where w is work done. Internal energy is a state function, as it only depends on the current state of the system.

Step 4: Analyzing Option (c) Q/w

Q/w represents the ratio of heat to work, which can vary with different paths taken in a process. This means it is not a state function.

Step 5: Analyzing Option (d) Q+w

Q+w represents the total energy of heat and work, which is a path-dependent quantity and not a state function. Total energy depends on how the heat and work are transferred.

Step 6: Conclusion

Based on the analysis, the only option that corresponds to a state function is option (b) Q-w, which represents the change in internal energy, a property that depends only on the state of the system.

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics is a fundamental principle that states energy cannot be created or destroyed, only transformed or transferred. This principle is also known as the Law of Conservation of Energy. In simple terms, the energy of an isolated system remains constant.

• It accounts for the internal energy change in a system due to heat added and work done.
• The formula representing this law is \(\Delta U = Q - W\), where \(\Delta U\) is the change in internal energy, \(Q\) is the heat added to the system, and \(W\) is the work done by the system.
• This law is foundational in understanding energy transfer in both physical and chemical processes.

The First Law is crucial in engineering, thermodynamics, and understanding chemical reactions. It reminds us of the conservation of energy – everything comes from something and goes somewhere.

Internal Energy

Internal energy is a state function that represents the total energy contained within a system. It includes kinetic and potential energies of the molecules within the system.

• It is denoted as \(U\) and measured in joules.
• Internal energy changes when heat is added or work is done on or by the system.
• Since it is a state function, its value depends only on the system's current state, not on how it reached that state.

Understanding internal energy helps in analyzing how systems behave under different conditions, such as heating or compressing gases. When \(\Delta U = Q - W\), you can see how energy transfers affect changes within the system.

Enthalpy

Enthalpy (H) is a thermodynamic property that takes into account both internal energy and the energy required to displace its environment to accommodate the system's pressure and volume. Enthalpy is useful in processes occurring at constant pressure.

• It is defined as \(H = U + PV\), where \(P\) is pressure, \(V\) is volume, and \(U\) is internal energy.
• Enthalpy changes, denoted \(\Delta H\), are often used in calculations of heat exchange at constant pressure.
• At constant pressure, enthalpy change equals the heat absorbed or released.

This concept is particularly important in chemistry and engineering for studying energy transfer in chemical reactions and phase changes, helping us evaluate whether processes are endothermic or exothermic.

Entropy

Entropy is a measure of the disorder or randomness in a system and is also a state function. It gives insight into the feasibility of a process.

• Entropy is represented by the symbol \(S\) and is often measured in joules per kelvin (J/K).
• An increase in entropy corresponds to an increase in disorder; conversely, a decrease indicates more order.
• In any spontaneous process, the total entropy of a system and its surroundings always increases.

The concept of entropy helps predict whether a process can occur spontaneously. It relates to the Second Law of Thermodynamics, emphasizing that natural processes tend to move towards higher disorder, underlying why ice melts or why gases expand.