42
2 Work, Heat, and Energy: The First Law of Thermodynamics
where P is the pressure of the gas and A is the area of the piston. We define the external
pressure P ext by
P ext
F ext
A
(definition of P ext )
(2.1-7)
At equilibrium there is no tendency for the piston to move so that
P P ext P(transmitted) (at equilibrium)
(2.1-8)
where we define the transmitted pressure by
P(transmitted)
F (transmitted)
A
(2.1-9)
A reversible process is defined to be one that can be reversed in direction by an
infinitesimal change in the surroundings. In order for an infinitesimal change in P ext
to change the direction of motion of the piston, there can be no friction and there
can be no more than an infinitesimal difference between P, P(transmitted), and P ext .
For an infinitesimal step of a reversible process the work done on the surroundings is
given by
dw surr,rev PdV (reversible process)
(2.1-10)
where V is the volume of the system. We will consistently use a subscript “surr” when a
symbol pertains to the surroundings. If no subscript is attached to a symbol, the symbol
refers to the system.
If a fluid system contains a single substance in a single phase, its equilibrium state
can be specified by the values of three variables such as T , V , and n. We can define
a three-dimensional space in which T , V , and n are plotted on the three axes. We call
such mathematical space a state space. Each equilibrium state is represented by a state
point located in the state space. A reversible process proceeds infinitely slowly, so that
the system has sufficient time to come to equilibrium during any part of the process.
The system passes through a succession of equilibrium states and the state point traces
out a curve in the equilibrium state space, such as that shown in Figure 2.3 for a fixed
value of n.
We reckon work done on the surroundings as a negative amount of work done on
the system, so we write
dw rev −PdV
(2.1-11)
The signs we have used correspond to the following convention: A positive value of w
or dw corresponds to work being done on the system by the surroundings. A negative
value of w or of dw corresponds to work being done on the surroundings by the system.
Unfortunately, the opposite convention has been used in some older books. We will
consistently use the convention stated above.
We have obtained the relation of Eq. (2.1-11) for a gas in a cylinder with a movable
piston. We assert that this relation applies to a fluid system of any shape. If a system
can exchange work with its surroundings only by changing its volume, we say that it
is a simple system. This kind of work is sometimes called compression work or P-V
work. A gas is a simple system. A liquid is a simple system if the work required to
create surface area by changing the shape of the system can be neglected. A spring or
a rubber band is not a simple system because work is done to change its length. An
electrochemical cell is also not a simple system since work can be done by passing a
current through it.
2 Work, Heat, and Energy: The First Law of Thermodynamics
where P is the pressure of the gas and A is the area of the piston. We define the external
pressure P ext by
P ext
F ext
A
(definition of P ext )
(2.1-7)
At equilibrium there is no tendency for the piston to move so that
P P ext P(transmitted) (at equilibrium)
(2.1-8)
where we define the transmitted pressure by
P(transmitted)
F (transmitted)
A
(2.1-9)
A reversible process is defined to be one that can be reversed in direction by an
infinitesimal change in the surroundings. In order for an infinitesimal change in P ext
to change the direction of motion of the piston, there can be no friction and there
can be no more than an infinitesimal difference between P, P(transmitted), and P ext .
For an infinitesimal step of a reversible process the work done on the surroundings is
given by
dw surr,rev PdV (reversible process)
(2.1-10)
where V is the volume of the system. We will consistently use a subscript “surr” when a
symbol pertains to the surroundings. If no subscript is attached to a symbol, the symbol
refers to the system.
If a fluid system contains a single substance in a single phase, its equilibrium state
can be specified by the values of three variables such as T , V , and n. We can define
a three-dimensional space in which T , V , and n are plotted on the three axes. We call
such mathematical space a state space. Each equilibrium state is represented by a state
point located in the state space. A reversible process proceeds infinitely slowly, so that
the system has sufficient time to come to equilibrium during any part of the process.
The system passes through a succession of equilibrium states and the state point traces
out a curve in the equilibrium state space, such as that shown in Figure 2.3 for a fixed
value of n.
We reckon work done on the surroundings as a negative amount of work done on
the system, so we write
dw rev −PdV
(2.1-11)
The signs we have used correspond to the following convention: A positive value of w
or dw corresponds to work being done on the system by the surroundings. A negative
value of w or of dw corresponds to work being done on the surroundings by the system.
Unfortunately, the opposite convention has been used in some older books. We will
consistently use the convention stated above.
We have obtained the relation of Eq. (2.1-11) for a gas in a cylinder with a movable
piston. We assert that this relation applies to a fluid system of any shape. If a system
can exchange work with its surroundings only by changing its volume, we say that it
is a simple system. This kind of work is sometimes called compression work or P-V
work. A gas is a simple system. A liquid is a simple system if the work required to
create surface area by changing the shape of the system can be neglected. A spring or
a rubber band is not a simple system because work is done to change its length. An
electrochemical cell is also not a simple system since work can be done by passing a
current through it.