State functions change

These two features of state functions are more important for scientists than for cross-counhy travelers like the Daltons. Chemists determine values of state function changes by doing careful experiments using convenient paths. These values are collected in tables, just as distances between cities are collected in an atlas. Energy is one such state function, and chemists use tabulated energy values to analyze chemical processes from a thermodynamic point of view. 

C14-0120. In a system operating without any restrictions, heat is not a state function. However, heat flow describes a state function change under certain restricted conditions. For each of the following conditions, identify the state function that corresponds to heat flow (a) gy, (b) qp and (c) qp. 

Because G and H are state functions, changes in these quantities are independent of whether the reaction takes place in one or in several steps. Consequently, it is possible to tabulate data for relatively few reactions and use this data in the calculation of AG° and AH0 for other reactions. In particular, one tabulates data for the standard reactions that involve the formation of a compound from its elements. One may then consider a reaction involving several compounds as being an appropriate algebraic sum of a number of elementary reactions, each of which involves the formation of one compound. The dehydration of n-propanol... 

When the stretched rubber band is relaxed, the signs of the thermodynamic state functions change ... 

Thermodynamic state functions change with temperature this will be true if values of the heat capacity of any component is nonzero (which is almost always true). Whenever the heat capacity is not a constant, the various thermodynamic state functions will show nonlinear dependencies on temperature. 

Entropy is a state function -> Changing the path does not change AS. 

The state of a quantum-mechanical system is described by a state function or wave function which is a function of the coordinates of the particles of the system and of the time. The state function changes with time according to the time-dependent Schrodinger equation, which for a one-particle, one-dimensional system is Eq. (1.13). For such a system, the quantity (x, i dx gives the probability Ibat a measurement of the particle s position at time t will find it between x and x H- djc.Hie state function is normalized according to = 1. If the system s potential-energy function... 

A uniform thermodynamic system—(uniform) body—may be visualized as a block of single (i.e., pure or one-constituent) material, the mass of which is fixed (closed system) with properties depending only on time (and not on space). Therefore, the state and state functions change only in time. Results (1.5) and (1.42) (where it is possible to use time integration) may be expressed in the rate form as it was explained at the end of Sect. 1.4. Consequently, such forms of energy balance and entropy inequality in uniform systems are [1, 3, 4]... 

In this chapter we have developed the first and second laws for closed and open systems. For closed systems both laws are motivated by the desire to relate the process variables Q and W to changes in system properties. To emphasize this common theme, we have stated each law in two parts part 1 defines a new state function (either U or S) and part 2 imposes limitations on how the new state function changes with certain changes of state. For closed systems, the first law asserts that an exact differential (dU) is obtained from the algebraic sum of 8Q and 5W while the second law asserts that an exact differential (dS) is obtained by appl3fing an integrating factor to If a quantity forms an exact differential, then it is a system property, and changes in its value are not affected by the process that cormects two states. 

Strategy Because entropy is a state function, changes in entropy are independent of the path taken therefore, we can assume that the expansion occurs reversibly for the purposes of calculating A5, allowing us to use Equation 8.9. 

State function change General expression Approximate expression Ideal gas for liquid or solid... 

There exists a state function S, called the entropy of a system, related to the heat Dq absorbedfrom the surroundings during an infinitesimal change by the relations... 

The are many ways to define the rate of a chemical reaction. The most general definition uses the rate of change of a themiodynamic state function. Following the second law of themiodynamics, for example, the change of entropy S with time t would be an appropriate definition under reaction conditions at constant energy U and volume V ... 

The state variables are the smallest number of states that are required to describe the dynamic nature of the system, and it is not a necessary constraint that they are measurable. The manner in which the state variables change as a function of time may be thought of as a trajectory in n dimensional space, called the state-space. Two-dimensional state-space is sometimes referred to as the phase-plane when one state is the derivative of the other. 

The second thing to note about the thermodynamic variables is that, since they are properties of the system, they are state functions. A state function Z is one in which AZ = Zi — Z that is, a change in Z going from state (l) to state (2), is independent of the path. If we add together all of the changes AZ, in going from state (1) to state (2), the sum must be the same no matter how many steps are involved and what path we take. Mathematically, the condition of being a state function is expressed by the relationship... 

Equation (1.4) states that if we add together all of the infinitesimal changes dZ over a closed path, the sum is equal to zero. This is a necessary condition for a state function. 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

If one causes an infinitismal change dZ to occur, the quantity dZ is an exact differential (whenever Z is a state function). We will now describe the test that determines if a differential is exact and summarize the relationship between exact differentials. 

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