CHAPTER 4. THERMODYNAMICS: THE FIRST LAW

4-2
how the change of state was carried out. Therefore, the changes in the values of the state functions
are determined only by the initial and final states of the system. For example, consider the four states
of a system composed of an ideal gas, as depicted in Fig. 4-1.
path 1
State 2
P 2
= 2 atm
V 2
= 22 L
T 2
= 546 K
State 1
P 1
= 1 atm
V 1
= 22 L
T 1
= 273 K
path 3
State 4
P 4
= 2 atm
V 4
= 11 L
T 4
= 273 K
path 2
State 3
P 3
= 1 atm
V 3
= 11 L
T 3
= 136 K
Figure 4-1. Transformation of a system from state 1 to state 4 via three different paths.
Three different paths lead from state 1 to state 4. However, the changes in all three of the state
functions listed (P, V, and T) are the same for each path. Going from state 1 to state 4 via path 1,
path 2, or path 3 results in P = 1 atm, V = 11 L, and T = 0 K. In other words, the final value
of a state function does not depend on the path taken between the initial and final state. On
the other hand, suppose that instead of different states of a system, the above (state) labels
represented different cities on a map and the three paths represented different routes between them.
It is obvious that distance is not a state function since the distance between city 1 and city 4 depends
on the route taken. In the city analogy, is altitude a state function? Of course distance is not a
thermodynamic variable, but two very important thermodynamic variables that are not state
functions are work and heat.
C. Work and heat