A reversible expansion can be devised by first recognizing that at any point
between the initial and final state, the gas must always be in equilibrium
with its surroundings. The equilibrium condition in this case is that the
internal gas pressure must equal the external pressure during the entire
process. The reversible process must be done such that this condition is
met in going from state A to state B. To understand the reversible expansion better, let’s do this process in a series of steps, as illustrated in Figure
2.7. Initially (state A) the gas pressure within the cylinder is 2 atm. Tiny
weights added to the top of the piston exert an external pressure of 2 atm.
The system is in equilibrium. Now imagine that one of these tiny weights is
removed such that the external pressure drops to 1.999 atm. The piston
moves up and the internal pressure drops to 1.999 atm (State B). Again,
this system is in equilibrium with its surroundings. The removal of an
additional weight further reduces the external and internal pressure to
1.998 atm (State C). These steps can be repeated until the final state is
reached in which the external and internal pressure is 1 atm. In true
reversible processes we would have an infinite number of steps in which
the pressure is reduced infinitesimally in going from state A to the final state.
Purely reversible processes are hypothetical, but like the types of ideal
systems and processes discussed earlier in the chapter, they are useful
approximations to real systems and allow derivation of important
relationships in thermodynamics. Processes can be carried out slowly and
P = 2 atm
P = 1.999 atm
Step 1
P = 1.998 atm
Step 2
Infinite number of steps
P = 1 atm
State A
State B
State C
Final state
Figure 2.7 The hypothetical concept of reversibility. The removal of weights from
the piston in infinitesimal amounts takes the system from its initial to final state.
Conversely, infinitesimal weights could be added onto the piston to reverse the
process. Each step is essentially in a state of equilibrium with the external pressure
exactly equal to the internal pressure of the gas in the piston.
THE FIRST LAW OF THERMODYNAMICS
31
between the initial and final state, the gas must always be in equilibrium
with its surroundings. The equilibrium condition in this case is that the
internal gas pressure must equal the external pressure during the entire
process. The reversible process must be done such that this condition is
met in going from state A to state B. To understand the reversible expansion better, let’s do this process in a series of steps, as illustrated in Figure
2.7. Initially (state A) the gas pressure within the cylinder is 2 atm. Tiny
weights added to the top of the piston exert an external pressure of 2 atm.
The system is in equilibrium. Now imagine that one of these tiny weights is
removed such that the external pressure drops to 1.999 atm. The piston
moves up and the internal pressure drops to 1.999 atm (State B). Again,
this system is in equilibrium with its surroundings. The removal of an
additional weight further reduces the external and internal pressure to
1.998 atm (State C). These steps can be repeated until the final state is
reached in which the external and internal pressure is 1 atm. In true
reversible processes we would have an infinite number of steps in which
the pressure is reduced infinitesimally in going from state A to the final state.
Purely reversible processes are hypothetical, but like the types of ideal
systems and processes discussed earlier in the chapter, they are useful
approximations to real systems and allow derivation of important
relationships in thermodynamics. Processes can be carried out slowly and
P = 2 atm
P = 1.999 atm
Step 1
P = 1.998 atm
Step 2
Infinite number of steps
P = 1 atm
State A
State B
State C
Final state
Figure 2.7 The hypothetical concept of reversibility. The removal of weights from
the piston in infinitesimal amounts takes the system from its initial to final state.
Conversely, infinitesimal weights could be added onto the piston to reverse the
process. Each step is essentially in a state of equilibrium with the external pressure
exactly equal to the internal pressure of the gas in the piston.
THE FIRST LAW OF THERMODYNAMICS
31