**THERMODYNAMICS
I**

**Scope
of thermodynamics**

Thermodynamics is a study and a sub division in pure physical science. It deals with the change or transformations of all types of energy. Most of the time it deals with the relationship between heat and the work relationship with other forms of energy with respect to flow of these other form of energy. There are different forms of energy.

Energy can be found in everything. There are even forms of energy that are not even found in the three basic states of matter, so you can imagine how vast energy apply to everything. It cannot be denied that the relationship between energy has become quite the study. The learning of how the transformation of energy is done has; aided man in the creation of relatively all the mechanical age machines, It has also helped chemists to understand reactions better, it has aided efficiency in all field of physical sciences.

By expanding the fore mentioned use of energy transfer you would get the idea of how important thermodynamics is, it you have not, you can always research.

**The axioms of thermodynamics**

After extensive study of thermodynamics through time, some basic laws has been validated. These laws has been tested through vast experience and tests in the real practical works, with some calculations (though for study sake no one will admit it). These laws are expressed in mathematical forms for easier approach to answers, hence making measurement in thermodynamics more efficient. Studying thermodynamics is based on four main postulates and axioms from which a wide range of governing laws are established

* First
axiom*. A form of energy known as
internal energy (U) can be found in substances. For systems at
equilibrium these form of energy is intrinsic property of the system
functionality, which is related to measurable co-ordinates that
describe the system. The down side of this is that the energy cannot
be measured directly.

* Second
axiom*. All the energy of a system
and its environment is conserved (cannot be created or destroyed),
this is the first law of thermodynamics and is stated mathematically
as thus;

ΔU_{total
}= 0

* Third
axiom*. In a system there is a
property called Entropy (S). This property for systems at
equilibrium, is related by function, to the measurable co-ordinates
that describes the system. Like the first the downside is, entropy
cannot be measured directly.

* Fourth
axiom*. When there is an entropic
change between the system and its environment it is worked on
together. Entropic change that is resulted from any real life event
or process is positive, and tends to a limiting value of zero as the
process approaches reversibility. This is the second law of
thermodynamics. This is stated as thus;

ΔS_{total
}≥ 0

Through combination of these axioms it can be deduced that

Energy can change forms i.e. it can transform from one form to another

The entropy of a separate, isolated system cannot change

Energy can be conserved

As you might have noted, the first and second axioms concentrated on the first law of thermodynamics. The third and fourth axioms (especially the fourth), emphasised on the second law of thermodynamics.

**The
System and its Environment**** **

**Universe****:
**The universe in thermodynamics is the
total environment where what is being studied can be found. (System +
Surrounding + Boundary)

**Boundary****:
**The boundary in thermodynamics limit or
edge of a system of a system in study, and the beginning of the
surrounding.

**Surrounding****:
**After the boundary of a system, the
environment the system interacts with is called the surrounding.

**System****:
**The system is the area of focus, where
most of the work is done.

**Terms
in systems and surroundings**** **

**Open****
(flow): **This is when there is a system
boundary that does allow flow of heat and other type of energy to and
from a system and its surrounding.

**Closed
(non-flow): **This is when there is a
system boundary that does not allow flow of heat and other type of
energy to and from a system and its surrounding. Heat might be
excluded from the forms of energy.

**Isolated
system: **These are closed systems that
are so insulated, that even heat cannot be transferred in or out of a
system.

**Process in thermodynamics **

**Isobaric****
or Isopiestic process: **This is a process that has a
constant pressure when it is being carried out. i.e. (Δp = 0)

= constant

=

**Isothermal
process: **This is a process that has a constant temperature
when it is being carried out. i.e. (ΔT = 0)

PV = Constant

P_{1}
V_{1 = }P_{2
}V_{2}

**Isometric
or Isochoric process: **This is a process that has a
constant volume when it is being carried out. i.e. (ΔV = 0)

**Anabatic:
**The process change
in heat is equal to zero.

PV^{r}
= Constant

P_{1}
V_{1}^{r
=} P_{2}
V_{2}^{r
}

^{r}

**Polytrophic
process: **In this
process, there is no special condition attached, it is also
subdivided, but I will not get into it here.

**THE RELATIONS IN THERMODYNAMICS**

Work done (W) = PΔV

= PdV

Heat (Q) = RTinV

= MCΔT

Enthalpy
(H) = C_{p}ΔT

Heat at constant volume (during isometric process) = Internal energy (U)

Heat at constant pressure (during isobaric process) = Enthalpy (H)

**The first law of thermodynamics**

ΔU= ΔQ – ΔW

ΣQ= ΣW

, ΔQ-ΔW= 0

**Closed
system:** ΔU= ΔQ +
ΔW

**Work
done: **W= PΔV

**The concept of Entropy**

The combination of two energy terms and properties of systems and thermodynamics.

H= U + PV = Q

ΔH= ΔQ

ΔW=
H_{2}-H_{1}

ΔW= PdV

ΔU=
C_{R}ΔT
or nC_{v}ΔT
(for when dealing with non-ideal gases that has numbers of molecule)
[n = number of moles]

ΔH=
C_{p}ΔT

ɣ= = constant

**Note**

In ideal gas, PV=nRT

**Derivatives **

V_{1
}=Initial volume_{
}

_{ }V_{2
}= Final volume

P_{1}
= Initial pressure

P_{2}
= Final pressure

T_{1
}= Initial Temperature

T_{2}
= Final Temperature

V_{!}^{r
}= Initial
volume_{ }at
gas constant

V_{2}^{r
}= final volume at gas constant

**Isothermal
process** (dT=0, P_{1}
V_{1 = }P_{2
}V_{2})

From first law of thermodynamics

dV= dQ-dW

C_{v}ΔT
= dQ- PdV

dT= 0

but PV= RT

P=

Q= W = V

= RT

=RT(_{V1}^{V2 }

=RT
(In V_{2 }–
In V_{1})

=
RTIn (V_{2}/V_{1})

But
(V_{2}/V_{1})
= (P_{1}=
P_{2})

**Isometric
process **(dV = 0,

From first law of thermodynamics

dV= dQ- dW

dW= PdV= 0

dQ=
dU= C_{v}ΔT

ΔH=
C_{p}ΔT

**Isobaric
process **(dP= 0,)

dU= dQ= dW

dH= dU + d(PV) =dU + d(RT)

dH= dU+ RdT

C_{p}ΔT=
C_{r}ΔT+
RΔT

Divide through by ‘ΔT’

[C_{p}
= C_{r }+
R)

Divide
through by ‘C_{r}’

_{
}

_{=
}ɣ-1

That means

_{
}

By substituting

C_{P}=
_{+
}
_{
}=
_{
}= R= R_{r
}–R =