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Chapter 9: Problem 11

Explain what is meant by a state function.

Short Answer

Expert verified
Answer: A state function in thermodynamics is a property that depends only on the current state of the system and is independent of the path taken to reach that state. It is determined by factors such as temperature, pressure, and composition. State functions describe the equilibrium state of a system and have properties like independence of path, exact differentials, and the ability to be combined with other state functions. On the other hand, path functions depend on the path taken to reach a particular state and are not determined solely by the initial and final states of the system. Examples of state functions include internal energy, enthalpy, entropy, Gibbs free energy, and Helmholtz free energy, while examples of path functions include work and heat.

Step by step solution

01

Definition of a State Function

In thermodynamics, a state function is a property that depends only on the current state of the system, which means it is independent of the path taken to reach that state. It is determined by factors such as temperature, pressure, and composition. State functions are used to describe the equilibrium state of a system.
02

Properties of a State Function

The main properties of a state function are: 1. It depends only on the initial and final states of the system. 2. It is independent of the path taken. 3. It obeys the property of exact differentials, meaning that its differential is an exact differential. 4. State functions can be added, subtracted, or combined to form new state functions.
03

State Functions vs. Path Functions

A state function is different from a path function. A path function depends on the path taken to reach a particular state and is not determined solely by the initial and final states of the system. Work and heat are examples of path functions.
04

Examples of State Functions

Examples of state functions in thermodynamics include: 1. Internal energy (U) 2. Enthalpy (H) 3. Entropy (S) 4. Gibbs free energy (G) 5. Helmholtz free energy (A) By understanding these concepts and the properties of state functions, one can better analyze thermodynamic processes and predict changes in a system based on its initial and final states.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamics
Thermodynamics is a branch of physics that studies the relationships between heat, work, temperature, and energy. It provides a framework for understanding how energy is transferred in physical and chemical processes.
  • Energy transfer: Thermodynamics explores how energy flows into and out of systems, impacting the system's conditions and function.
  • State functions: These include properties like internal energy, enthalpy, and entropy that depend only on the system's state and not the path taken to reach that state.
  • Path functions: Unlike state functions, these are dependent on how the system evolves. Examples include work and heat.
The laws of thermodynamics govern these interactions and valid transformations between different forms of energy.
Understanding these principles helps in predicting the behavior of systems as they undergo various processes, such as heating, cooling, or changes in volume.
Equilibrium State
An equilibrium state in thermodynamics represents a state where a system's macroscopic properties do not change with time. The system has achieved balance, showing no net change in energy or matter's flow.
  • Dynamic equilibrium: Even though macroscopic properties are constant, molecules are in continuous motion, maintaining balance through dynamic processes.
  • Thermal equilibrium: Occurs when two systems in contact reach the same temperature, resulting in no net flow of heat.
  • Mechanical equilibrium: Forces are balanced, leading to no physical change in the system's position or structure.
Understanding equilibrium is key to predicting how systems react to changes in condition, ensuring accurate thermodynamic calculations.
Equilibrium states help in assessing when a system has 'settled' and is no longer altering its internal energy conditions.
Enthalpy
Enthalpy, denoted as \( H \), is a state function representing the total heat content of a system. It reflects the capacity for doing work and hosting energy changes in biochemical and physical processes.
  • Formula: Enthalpy is described as \( H = U + PV \), where \( U \) is internal energy, \( P \) is pressure, and \( V \) is volume.
  • Characteristics: As a state function, enthalpy relies solely on the current state, presenting a clear picture of heat transfer under constant pressure.
  • Applications: It's crucial in calculating energy changes in reactions and phase transitions, including heat released or absorbed.
Enthalpy changes help understand reaction dynamics, particularly in exothermic and endothermic processes.
By monitoring enthalpy, one can predict if a process will release or require energy, assisting in energy management strategies.
Entropy
Entropy, symbolized as \( S \), is a measure of disorder or randomness in a system. It's a fundamental concept in thermodynamics expressing energy loss and dispersion in processes.
  • Second Law of Thermodynamics: Entropy is often associated with this law, stating that in any spontaneous process, the total entropy of a closed system will tend to increase.
  • Formula: The change in entropy is given by \( \Delta S = \frac{q_{rev}}{T} \), where \( q_{rev} \) is reversible heat exchange and \( T \) is temperature.
  • Significance: It helps in determining the feasibility and direction of chemical and physical processes.
Higher entropy signifies greater disorder, often used as an indicator of energy system efficiency.
In evaluating entropy, scientists can assess how energy transforms across different forms, predicting the sustainability and spontaneity of processes.

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Most popular questions from this chapter

Oxygen and ozone are both forms of elemental oxygen. Are the standard heats of formation of oxygen and ozone the same? Why or why not?

At high temperatures, such as those in the combustion chambers of automobile engines, nitrogen and oxygen form nitrogen monoxide: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g) \quad \Delta H_{\mathrm{comb}}^{\circ}=+180 \mathrm{kJ}$$ Any NO released into the environment may be oxidized to \(\mathrm{NO}_{2}:\) $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H_{\mathrm{comb}}^{\circ}=-112 \mathrm{kJ}$$ Is the overall reaction, $$\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ exothermic or endothermic? What is \(\Delta H_{\text {comb }}^{\circ}\) for this reaction?

An expanding gas does \(150.0 \mathrm{J}\) of work on its surroundings at a constant pressure of 1.01 atm. If the gas initially occupied \(68 \mathrm{mL},\) what is the final volume of the gas?

A coffee-cup calorimeter contains \(100.0 \mathrm{mL}\) of \(1.00 M \mathrm{HCl}\) at \(22.4^{\circ} \mathrm{C} .\) When \(0.243 \mathrm{g}\) of \(\mathrm{Mg}\) metal is added to the acid, the ensuing reaction: $$\mathrm{Mg}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g) \quad \Delta H_{\mathrm{rxn}}=?$$ causes the temperature of the solution to increase to \(33.4^{\circ} \mathrm{C}\) What is the value of \(\Delta H_{\mathrm{rxn}}\) of the reaction? Assume the density of the solution is \(1.01 \mathrm{g} / \mathrm{mL}\) and that its specific heat is \(4.18 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right)\).

If the energy needed to break two moles of \(\mathrm{C}=\mathrm{O}\) bonds is greater than the sum of the energies needed to break the \(\mathrm{O}=\mathrm{O}\) bonds in one mole of \(\mathrm{O}_{2}\) and vaporize one mole of carbon, why does the combustion of pure carbon release heat?
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