Introductory thermodynamics
summary
By Emma Burgwal
CHAPTER 1
Heat is a form of energy transfer and scientists therefore published the first and second law of
thermodynamics. Thermodynamics is the science concerned with the transformation of energy.
Thermodynamics tells you which processes are possible and which aren’t. The first law states that
processes are only possible when energy is conserved and the second law states that processes must
produce entropy.
The first law says that energy can be converted into other forms of energy, provided the total energy
of system and surroundings remains constant.
Entropy is the measure for energy dispersal (related to the number of ways to distribute energy).
Entropy is a property of a system. In cyclic processes, entropy must also increase, however, the initial
and final entropy if the system are the same. Entropy in the surroundings must have increased.
Entropy is generated or produced and energy is conserved.
Natural or spontaneous processes proceed without intervention. Spontaneous processes always
proceed in a specific direction which is coupled to the production of entropy. A process is irreversible
if the process produces entropy. A process is reversible if it produces no entropy. A reversible
process must evolve through an infinite number of equilibrium states. These processes don’t exist in
reality, but they can serve as a reference in assessing the quality of real life processes.
In a closed system, energy can be exchanged by way of heat and work. The first law (energy is
conserved): ΔU =Q+W . A positive value of Q means that heat flows into the system. U is the
difference between final and initial state. The symbol Δ is used for state functions. Heat and work are
no properties of a system and thus no state functions. A variable is a state function if its value is
coupled to the state of a system and not to a process. The first law can be written in terms of energy
flow rates (divided by dt). dU =dQ +dW , is the first law in differential form.
Volume work (mechanical work) can be described in an equation: Wvol=−Pe∗dV , which can be
integrated to the form dWvol=−Pe∗dV . The first law can be written as:
dU =dQ −Pe∗dV + dWother .
Extensive parameters (like volume) are connected to the size of a system. Intensive parameters are
insensitive to the size (like pressure). If Y is an extensive parameter, then the corresponding molar
Y
quantity Ym is given by Ym= , where n is the total amount of substance in a system.
n
Storage of newly created entropy diS: diS =ds−deS , where deS are the surroundings. The energy
production is a system always equals 0, since energy can’t be produced or destroyed.
The total increase in the quantity Y is due to the production is Y in system and surroundings. The i in
equation stands for internal, the e stands for exchange. Entropy can only be produced, so diS is
dQ
greater than zero. An equation for the entropy change can be derived: dS= , which is only true
T
for reversible processes. This equation can be applied for the idealized surroundings, giving:
dQ dQ
deS= , so the second law follows as dS=diS+ . If a process is adiabatic, the entropy of the
Te Te
system must increase. Otherwise, it can decrease (if the surroundings increase), for example in a
cyclic process.
, Ideal or perfect gasses have no volume and don’t interact with each other. This makes that an ideal
gas can be compressed in an arbitrary small volume. The ideal gas equation goes as followed:
PV =nRT . There is only kinetic energy in an ideal gas.
3 1
Mono-atomic gas: ΔU = nRΔT and the expansion coefficient: α = ¿ ). Combining gives:
2 V
P
∗nR
nRT 1.
α= =
P T
CHAPTER 2
It requires more heat to raise the temperature at constant pressure than at constant volume,
because the system expands when it gets hotter at constant pressure. This is the situation with
gasses. With liquids and solids, part of the supplied heat is stored as intermolecular interaction
energy.
Heat capacity is the heat needed to increase the temperature by 1 Kelvin. To be safe, we determine
δQ
the heat capacity under small temperature changes: C= . The volume is equal to 0 at constant
δT
volume, which defines the heat capacity as : Cv= ( δUδT ) V , n. N is constant, because of the first law.
Cv can be divided by n to get a molar quantity Cv,m.
At constant pressure, the first law can be rewritten as dQ =d (U + PV ), where the U + PV is a state
function on its own called enthalpy (H = U + PV). Energy is mixed with volume and pressure with
enthalpy. For reversible changes at constant pressure dQ = dH. This holds true also for irreversible
processes at external pressure. Cp= ( δHδT ) P , n, where Cp can be divided by n to get Cp,m.
A system is adiabatic if there is no heat exchange (Q is zero and ΔU = W).
A system is isochoric if it has no change in volume (dU = dQ). An example of this system is a bomb
calorimeter.
A process is isobaric if it occurs at constant internal pressure (ΔH = Q).
A system can be reversibly heated and the entropy follows as: ΔS =∫ dQ/ T , combining with heat
T2
capacity integrates to ΔS =Cvln . Here, Cv should be constant, the temperatures should be at
T1
equilibrium and should have the same volume.
CHAPTER 3
The first and second law can be combined to get a new equation:
dU =¿ Te∗diS+ Te∗dS−Pe∗dV +dWother and this equation can be reduced, if you have a
reversible process, to: dU =T∗dS−P∗dV +dWother (or without dW), because it produces no
entropy.
The first and second law can be combined with enthalpy, resulting in: dH =T∗dS+ V∗dP. The
Gibbs energy considers changes in pressure and temperature: G=H −TS and
dG =−S∗dT +V ∗dP .
CHAPTER 4
summary
By Emma Burgwal
CHAPTER 1
Heat is a form of energy transfer and scientists therefore published the first and second law of
thermodynamics. Thermodynamics is the science concerned with the transformation of energy.
Thermodynamics tells you which processes are possible and which aren’t. The first law states that
processes are only possible when energy is conserved and the second law states that processes must
produce entropy.
The first law says that energy can be converted into other forms of energy, provided the total energy
of system and surroundings remains constant.
Entropy is the measure for energy dispersal (related to the number of ways to distribute energy).
Entropy is a property of a system. In cyclic processes, entropy must also increase, however, the initial
and final entropy if the system are the same. Entropy in the surroundings must have increased.
Entropy is generated or produced and energy is conserved.
Natural or spontaneous processes proceed without intervention. Spontaneous processes always
proceed in a specific direction which is coupled to the production of entropy. A process is irreversible
if the process produces entropy. A process is reversible if it produces no entropy. A reversible
process must evolve through an infinite number of equilibrium states. These processes don’t exist in
reality, but they can serve as a reference in assessing the quality of real life processes.
In a closed system, energy can be exchanged by way of heat and work. The first law (energy is
conserved): ΔU =Q+W . A positive value of Q means that heat flows into the system. U is the
difference between final and initial state. The symbol Δ is used for state functions. Heat and work are
no properties of a system and thus no state functions. A variable is a state function if its value is
coupled to the state of a system and not to a process. The first law can be written in terms of energy
flow rates (divided by dt). dU =dQ +dW , is the first law in differential form.
Volume work (mechanical work) can be described in an equation: Wvol=−Pe∗dV , which can be
integrated to the form dWvol=−Pe∗dV . The first law can be written as:
dU =dQ −Pe∗dV + dWother .
Extensive parameters (like volume) are connected to the size of a system. Intensive parameters are
insensitive to the size (like pressure). If Y is an extensive parameter, then the corresponding molar
Y
quantity Ym is given by Ym= , where n is the total amount of substance in a system.
n
Storage of newly created entropy diS: diS =ds−deS , where deS are the surroundings. The energy
production is a system always equals 0, since energy can’t be produced or destroyed.
The total increase in the quantity Y is due to the production is Y in system and surroundings. The i in
equation stands for internal, the e stands for exchange. Entropy can only be produced, so diS is
dQ
greater than zero. An equation for the entropy change can be derived: dS= , which is only true
T
for reversible processes. This equation can be applied for the idealized surroundings, giving:
dQ dQ
deS= , so the second law follows as dS=diS+ . If a process is adiabatic, the entropy of the
Te Te
system must increase. Otherwise, it can decrease (if the surroundings increase), for example in a
cyclic process.
, Ideal or perfect gasses have no volume and don’t interact with each other. This makes that an ideal
gas can be compressed in an arbitrary small volume. The ideal gas equation goes as followed:
PV =nRT . There is only kinetic energy in an ideal gas.
3 1
Mono-atomic gas: ΔU = nRΔT and the expansion coefficient: α = ¿ ). Combining gives:
2 V
P
∗nR
nRT 1.
α= =
P T
CHAPTER 2
It requires more heat to raise the temperature at constant pressure than at constant volume,
because the system expands when it gets hotter at constant pressure. This is the situation with
gasses. With liquids and solids, part of the supplied heat is stored as intermolecular interaction
energy.
Heat capacity is the heat needed to increase the temperature by 1 Kelvin. To be safe, we determine
δQ
the heat capacity under small temperature changes: C= . The volume is equal to 0 at constant
δT
volume, which defines the heat capacity as : Cv= ( δUδT ) V , n. N is constant, because of the first law.
Cv can be divided by n to get a molar quantity Cv,m.
At constant pressure, the first law can be rewritten as dQ =d (U + PV ), where the U + PV is a state
function on its own called enthalpy (H = U + PV). Energy is mixed with volume and pressure with
enthalpy. For reversible changes at constant pressure dQ = dH. This holds true also for irreversible
processes at external pressure. Cp= ( δHδT ) P , n, where Cp can be divided by n to get Cp,m.
A system is adiabatic if there is no heat exchange (Q is zero and ΔU = W).
A system is isochoric if it has no change in volume (dU = dQ). An example of this system is a bomb
calorimeter.
A process is isobaric if it occurs at constant internal pressure (ΔH = Q).
A system can be reversibly heated and the entropy follows as: ΔS =∫ dQ/ T , combining with heat
T2
capacity integrates to ΔS =Cvln . Here, Cv should be constant, the temperatures should be at
T1
equilibrium and should have the same volume.
CHAPTER 3
The first and second law can be combined to get a new equation:
dU =¿ Te∗diS+ Te∗dS−Pe∗dV +dWother and this equation can be reduced, if you have a
reversible process, to: dU =T∗dS−P∗dV +dWother (or without dW), because it produces no
entropy.
The first and second law can be combined with enthalpy, resulting in: dH =T∗dS+ V∗dP. The
Gibbs energy considers changes in pressure and temperature: G=H −TS and
dG =−S∗dT +V ∗dP .
CHAPTER 4
