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Chapter 6: Problem 7

The internal energy of a substance is a state function. What does this mean?

Short Answer

Expert verified
Internal energy depends only on the initial and final states, not the path taken.

Step by step solution

01

Understanding State Function

A state function is a property whose value does not depend on the path taken to reach that specific value, but only on the initial and final states of the system. In thermodynamics, state functions include properties like internal energy, enthalpy, and entropy.
02

Internal Energy as a State Function

For internal energy, being a state function means that its change from an initial state to a final state is independent of the way the system acquired those states. Only the states themselves matter, not the process of changing states.
03

Implications of Internal Energy's Path Independence

Since internal energy is independent of the path, any process, whether it is slow, fast, constant volume, or constant pressure, between the same initial and final states will result in the same change in internal energy. This concept is crucial for simplifying calculations of energy changes in thermodynamics.

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Key Concepts

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

Internal Energy
Internal energy is a fundamental concept in thermodynamics. It refers to the total energy contained within a system. This includes all forms of kinetic and potential energy of the molecules within the system.
One of the key characteristics of internal energy is that it is a "state function." This means its value is determined solely by the current state of the system, not the path the system took to reach that state.
In practical terms:
  • The change in internal energy when a system moves from one state to another is the same regardless of the process used to make the change.
  • This property is extremely useful because it simplifies the calculations of energy exchanges in thermodynamics.
Understanding internal energy is crucial for studying how energy is transferred and transformed within different systems.
Thermodynamics
Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. This field is pivotal in understanding how energy transitions in various processes, from engines running to ice melting.
The principles of thermodynamics are built around a few key laws:
  • First Law of Thermodynamics: Also known as the law of energy conservation, it states that the total energy of an isolated system is constant.
  • Second Law of Thermodynamics: It dictates that energy transformations are not 100% efficient; some energy is always dispersed as heat.
Thermodynamics also categorizes properties of systems into two groups: state functions and path functions. Recognizing the difference between these types helps in analyzing energy exchanges in various processes.
Entropy
Entropy is a measure of the randomness or disorder within a system. In thermodynamics, it is another important state function.
Some crucial points about entropy include:
  • Entropy tends to increase in an isolated system. This tendency is aligned with the Second Law of Thermodynamics, which suggests that systems naturally progress towards disorder.
  • Entropy can be thought of as the possible number of ways a system can be arranged, with more disordered systems having higher entropy.
Entropy helps predict the direction of spontaneous processes and offers insight into the feasibility of chemical reactions and processes.
Enthalpy
Enthalpy is another vital concept in thermodynamics, often symbolized by the letter H. It represents the total heat content of a system at constant pressure.
Some key aspects of enthalpy include:
  • Because it is a state function, the change in enthalpy for a system undergoing a transformation depends only on its initial and final states.
  • Enthalpy is especially useful in chemical reactions, as it provides a straightforward measure of the heat absorbed or released.
Understanding enthalpy is critical for predicting the energy changes in chemical reactions and designing processes that require heat management.

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Most popular questions from this chapter

What is the phosphorus compound used in "strike anywhere" matches. What is the chemical equation for the burning of this compound in air?

The process of dissolving ammonium nitrate, \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), in water is an endothermic process. What is the sign of \(q ?\) If you were to add some ammonium nitrate to water in a flask, would you expect the flask to feel warm or cool?

Acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\), is contained in vinegar. Suppose acetic acid was formed from its elements, according to the following equation: $$ 2 \mathrm{C} \text { (graphite) }+2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(l) $$ Find the enthalpy change, \(\Delta H\), for this reaction, using the following data: $$ \begin{gathered} \mathrm{CH}_{3} \mathrm{COOH}(l)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H=-874 \mathrm{~kJ} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) ; \Delta H=-394 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) ; \Delta H=-286 \mathrm{~kJ} \end{gathered} $$

Given the following (hypothetical) thermochemical equations: $$ \begin{aligned} &\mathrm{A}+\mathrm{B} \longrightarrow 2 \mathrm{C} ; \Delta H=-447 \mathrm{~kJ} \\ &\mathrm{~A}+3 \mathrm{D} \longrightarrow 2 \mathrm{E} ; \Delta H=-484 \mathrm{~kJ} \\ &2 \mathrm{D}+\mathrm{B} \longrightarrow 2 \mathrm{~F} ; \Delta H=-429 \mathrm{~kJ} \end{aligned} $$ Calculate \(\Delta H\), in \(\mathrm{kJ}\), for the equation $$ 4 \mathrm{E}+5 \mathrm{~B} \longrightarrow 4 \mathrm{C}+6 \mathrm{~F} $$

A piece of lead of mass \(121.6 \mathrm{~g}\) was heated by an electrical coil. From the resistance of the coil, the current, and the time the current flowed, it was calculated that \(235 \mathrm{~J}\) of heat was added to the lead. The temperature of the lead rose from \(20.4^{\circ} \mathrm{C}\) to \(35.5^{\circ} \mathrm{C}\). What is the specific heat of the lead?
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