The Foundations of Chemistry

The thermodynamic state of a systemis defined by a set of conditions that completely
specifies all the properties of the system. This set commonly includes the temperature,
pressure, composition (identity and number of moles of each component), and physical
state (gas, liquid, or solid) of each part of the system. Once the state has been specified,
all other properties — both physical and chemical — are fixed.
The properties of a system — such as P, V, T— are called state functions.The value
of a state function depends onlyon the state of the system and not on the way in which
the system came to be in that state. A changein a state function describes a difference
between the two states. It is independent of the process or pathway by which the change
occurs.
For instance, consider a sample of one mole of pure liquid water at 30°C and 1 atm
pressure. If at some later time the temperature of the sample is 22°C at the same pres-
sure, then it is in a different thermodynamic state. We can tell that the nettemperature
change is 8°C. It does not matter whether (1) the cooling took place directly (either
slowly or rapidly) from 30°C to 22°C, or (2) the sample was first heated to 36°C, then
cooled to 10°C, and finally warmed to 22°C, or (3) any other conceivable path was followed
from the initial state to the final state. The change in other properties (e.g., the pressure)
of the sample is likewise independent of path.
The most important use of state functions in thermodynamics is to describe changes.
We describe the difference in any quantity, X,as

XXfinalXinitial

When Xincreases, the final value is greater than the initial value, so
Xis positive;a
decrease in Xmakes
Xa negativevalue.
You can consider a state function as analogous to a bank account. With a bank account,
at any time you can measure the amount of money in your account (your balance) in
convenient terms — dollars and cents. Changes in this balance can occur for several reasons,
such as deposit of your paycheck, writing of checks, or service charges assessed by the
bank. In our analogy these transactions are notstate functions, but they do cause changes
inthe state function (the balance in the account). You can think of the bank balance on a
vertical scale; a deposit of $150 changes the balance by$150, no matter what it was at
the start, just as a withdrawal of $150 would change the balance by$150. Similarly, we
shall see that the energy of a system is a state function that can be changed — for instance,
by an energy “deposit” of heat absorbed or work done on the system, or by an energy
“withdrawal” of heat given off or work done by the system.
We can describe differencesbetween levels of a state function, regardless of where the
zero level is located. In the case of a bank balance, the “natural” zero level is obviously
the point at which we open the account, before any deposits or withdrawals. In contrast,
the zero levels on most temperature scales are set arbitrarily. When we say that the temper-
ature of an ice–water mixture is “zero degrees Celsius,” we are not saying that the mixture
contains no temperature! We have simply chosen to describe this point on the tempera-
ture scale by the number zero;conditions of higher temperature are described by positive
temperature values, and those of lower temperature have negative values, “below zero.”
The phrase “15 degrees cooler” has the same meaning anywhere on the scale. Many of
the scales that we use in thermodynamics are arbitrarily defined in this way. Arbitrary
scales are useful when we are interested only in changesin the quantity being described.
Any property of a system that depends only on the values of its state functions is also
a state function. For instance, the volume of a given sample of water depends only on
temperature, pressure, and physical state; volume is a state function. We shall encounter
other thermodynamic state functions.

State functions are represented by

capital letters. Here Prefers to

pressure, Vto volume, and Tto

absolute temperature.

15-2 Some Thermodynamic Terms 595

Initial balance

$150

Final balance

Here is a graphical representation of a

$150 decrease in your bank balance.

We express the change in your bank

balance as 
$$final$initial. Your

final balance is lessthan your initial

balance, so the result is negative,

indicating a decrease.There are many

ways to get this same net change — one

large withdrawal or some combination

of deposits, withdrawals, interest

earned, and service charges. All of the


values we will see in this chapter can

be thought of in this way.

Increasing account balance

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