system. Since the temperature of the system remains constant, the change
in internal energy of the system must be zero in going from the initial to
the final state.
We can use these ideals to formulate a useful version of the First law of
thermodynamics. If work and heat are the only forms of energy transfer in
a system, then the change in internal energy of the system is given by
ΔE = q + w
(2.20)
Equation 2.20 is one statement of the first law of thermodynamics. We will
use it to obtain other thermodynamic relationships.
To illustrate an application of the first law, let’s considers the heating (or
cooling) of n moles of liquid water from T 1 to T 2 under conditions of constant
atmospheric pressure. The molar heat absorbed is given by Equation 2.21:
q P = n
C T 2 − T 1
ð
Þ
(2.21)
If T 2 > T 1 , q P is positive and heat is absorbed. The corresponding work
done for this process is
w = −P ext V 2 − V 1
ð
Þ
(2.22)
The volume of the water will not change very much for this process and
so the work done is practically zero. Thus, according to the first law
(Equation 2.20), the internal energy for the heat or cooling of water
depends only on the molar heating capacity of water and the temperature
difference (Equation 2.23):
Δ
E = n
C V T 2 − T 1
ð
Þ
(2.23)
Since the process is occurring at constant volume (no expansive work),
one only needs to know heat capacity and the temperature difference in
order to determine the change in internal energy. Comparing Equations
2.21 and 2.23, we immediately see that heat absorbed or lost is equal to
the change in molar internal energy,
q V = Δ
E
(2.24)
Since the heat capacity is defined as the derivative of q with respect to T
(see Equation 2.19), we have our formal definition of heat capacity at
constant volume (Equation 2.25):
C V =
∂ E
∂ T
V
(2.25)
We will use this fact to introduce another state function called enthalpy.
THE FIRST LAW OF THERMODYNAMICS
37
in internal energy of the system must be zero in going from the initial to
the final state.
We can use these ideals to formulate a useful version of the First law of
thermodynamics. If work and heat are the only forms of energy transfer in
a system, then the change in internal energy of the system is given by
ΔE = q + w
(2.20)
Equation 2.20 is one statement of the first law of thermodynamics. We will
use it to obtain other thermodynamic relationships.
To illustrate an application of the first law, let’s considers the heating (or
cooling) of n moles of liquid water from T 1 to T 2 under conditions of constant
atmospheric pressure. The molar heat absorbed is given by Equation 2.21:
q P = n
C T 2 − T 1
ð
Þ
(2.21)
If T 2 > T 1 , q P is positive and heat is absorbed. The corresponding work
done for this process is
w = −P ext V 2 − V 1
ð
Þ
(2.22)
The volume of the water will not change very much for this process and
so the work done is practically zero. Thus, according to the first law
(Equation 2.20), the internal energy for the heat or cooling of water
depends only on the molar heating capacity of water and the temperature
difference (Equation 2.23):
Δ
E = n
C V T 2 − T 1
ð
Þ
(2.23)
Since the process is occurring at constant volume (no expansive work),
one only needs to know heat capacity and the temperature difference in
order to determine the change in internal energy. Comparing Equations
2.21 and 2.23, we immediately see that heat absorbed or lost is equal to
the change in molar internal energy,
q V = Δ
E
(2.24)
Since the heat capacity is defined as the derivative of q with respect to T
(see Equation 2.19), we have our formal definition of heat capacity at
constant volume (Equation 2.25):
C V =
∂ E
∂ T
V
(2.25)
We will use this fact to introduce another state function called enthalpy.
THE FIRST LAW OF THERMODYNAMICS
37