THE FIRST LAW OF THERMODYNAMICS
1. INTRODUCTION
The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amount of matter. As we all know energy neither can be created nor destroyed, it is just transformed from one form to another. This is called the 'Law of conservation of energy '.The first law of thermodynamics is just an upgraded form of the law of conservation of energy. Energy is observed in various forms but basically, the energy is subdivided into two types i.e heat energy and thermodynamic work.
The first law of thermodynamics is formulated by ∆U=Q - W, Wherein ∆U denotes the change in internal energy of a closed system. Q denotes the quantity of energy supplied to the system as heat and W denotes the work done.
·
For
example,
2) Imagine someone putting an ice cube into a glass of warm water and then forgetting to drink it. An hour or two later, they will notice that the ice has melted but the temperature of the water has been cooled. This is because the total amount of heat in the system has remained the same.
2. HISTORY
In 1840,
Germain Hess stated a conservation law (Hess's Law) for the heat generated
during chemical reactions. This law was later recognized as a consequence of
the first law of thermodynamics, but Hess's has some drawbacks and that was a reason
he didn't get the credit for giving the first law of thermodynamics. The
first full statements of the law came in 1850 from Rudolf Clausius and William
Rankine. Some scholars consider Rankine's statement less accurate than that of
Clausius.
The first explicit statement of the first law of thermodynamics, by
Rudolf Clausius in 1850: In all cases in which work is produced by the agency
of heat, a quantity of heat is consumed which is proportional to the work done;
and conversely, by the expenditure of an equal quantity of work an equal
quantity of heat is produced.
After the number of research, the
revised statement given by the researchers is:-
For a closed system, in any
arbitrary process of interest that takes it from an initial to a final state of
internal thermodynamic equilibrium, the change of internal energy is the same
as that for a reference adiabatic work process that links those two states.
This is so regardless of the path of the process of interest, and regardless of
whether it is an adiabatic or a non-adiabatic process. The reference adiabatic
work process may be chosen arbitrarily from amongst the class of all such
processes.
This
statement is not much close to the empirical basis than the original
statements, Largely through the influence of Max Born,
this statement is theoretically preferable because of this conceptual
parsimony.
Basing his thinking on the mechanical approach in 1949, he proposed a revised
definition of heat. In particular, he referred to the work of Constantin Carathéodory, who had in 1909 stated the first
law without defining the quantity of heat. His definition mainly focused on the
transfer of energy neglecting the transfer of matter and is mostly preferred. Born
notes that when the matter is transferred between two systems, internal energy
that cannot be broken down into heat and work components is also transferred.
There may be connections to other systems that are geographically apart from
those of matter transmission and that provide simultaneous and independent heat
and work transfer with matter transfer. These transfers conserve energy.
3. CYCLIC PROCESS
Clausius provided two formulations of the first law of thermodynamics
for a closed system. The system's inputs, outputs, and cyclical processes were
all mentioned in one way, but no changes to the system's internal state. The
alternative strategy did not anticipate the process to be cyclical and instead
pointed to a gradual change in the system's internal state.
A cyclic process can be carried out repeatedly and endlessly, bringing
the system back to its starting point. The network completed and the net heat
absorbed (or "consumed," in Clausius' terminology), by the system,
are of special interest during a single cycle of a cyclic process.
4. SIGN CONVENTIONS
In a general process, the net energy added as heat to the system less
the thermodynamic work performed by the system, both measured in mechanical
units, equals the change in the internal energy of a closed system. Taking as the
change in internal energy.
where denotes the net quantity of heat supplied to the system by its
surroundings and denotes the net work done by the system. This sign convention
is implicit in Clausius' statement of the law given above. It originated with
the study of heat engines that produce useful work by consumption of heat; the key
performance indicator of any heat engine is its thermal efficiency, which is
the quotient of the net work done and the heat supplied to the system
(disregarding waste heat given off). Thermal efficiency must be positive, which
is the case if net work done and heat supplied are both of the same sign; by
convention, both are given the positive sign.
Nowadays, however, writers often use the IUPAC convention by which the
first law is formulated with thermodynamic work done on the system by its
surroundings having a positive sign. With this now often-used sign convention
for work, the first law for a closed system may be written:
Continuing in the Clausius sign convention for work, when a system
expands in a quasistatic process, the thermodynamic work done by
the system on the surroundings is the product, of pressure, and
volume change, whereas the thermodynamic work done on the
system by the surroundings is. Using either sign convention for work, the
change in internal energy of the system is:
where denotes the infinitesimal amount of heat supplied to the system
from its surroundings and denotes an inexact differential.
where denotes the infinitesimal amount of heat supplied to the system
from its surroundings and denotes an inexact differential. Thus the term
'heat' means "that amount of energy added or removed as heat in the thermodynamic
sense", rather than referring to a form of energy within the system.
Likewise, the term 'work energy' means "that amount of energy
gained or lost through thermodynamic work". Internal energy is a
property of the system whereas work done and heat supplied are not. A
significant result of this distinction is that a given internal energy change can
be achieved by different combinations of heat and work. (This may be signaled
by saying that heat and work are path dependent, while the change in internal
energy depends only on the initial and final states of the process. It is
necessary to bear in mind that thermodynamic work is measured by the change in
the system, not necessarily the same as work measured by forces and distances
in the surroundings;[25] this distinction is noted in
the term 'isochoric work'
5. EVIDENCE OF THE FIRST LAW OF THERMODYNAMICS
It was empirically observed data, such as calorimetric data, that led to
the original induction of the first law of thermodynamics for closed systems.
However, it is currently accepted to define work in terms of changes to a
system's external properties and to define heat using the law of conservation
of energy. The rule was first discovered gradually over maybe fifty years or
more, and some of the early investigations were done in terms of cyclic
processes.
The description that follows describes state changes in a closed system
caused by compound processes that aren't always cyclic. This description
initially takes into account adiabatic processes (in which there is no heat
transfer) and adynamic processes, for which the first law is easily confirmed
due to their simplicity (in which there is no transfer as work).
6. APPLICATIONS
1) Isobaric processes:-
The
first law of thermodynamics states that any change in the internal energy of a
given system (U) will be the same as the difference between the amount of
thermal energy added to that system (Q) and the network that is done by that
system (W).
Molar heat capacity is the heat given per mole per unit rise in the temperature
of a gas. If this thermal energy is supplied when pressure remains
constant, it is called Molar Heat Capacity at constant pressure.
This
is denoted by:- Cp=(△Qn△T)pCp=(△Qn△T)p,
where
the subscript ‘p’ denotes constant pressure. As discussed earlier, the heat
supplied to the gas in an isobaric process goes partially into increasing its
volume by a small amount (dV) and partially into increasing its internal energy
by (dU).
From
the First Law of Thermodynamics,
△Q=△U+△W△Q=△U+△W
Applying,
we get
(dQ)p = dU + PdV……. (i)
(at
constant volume dV = 0, therefore W=0, from the first law of thermodynamics
△Q=△U△Q=△U
or
heat supplied at constant volume = change in its internal energy). So, dU =
(dQ)v.
Therefore
equation
becomes,
(dQ)p = (dQ)v + PdV……. (ii)
For
an Ideal Gas, PV = nRT,
Therefore,
PdV = nRdT,
So, (dQ)p = (dQ)v + nRdT……. (iii)
From
here we also can
prove
Cp
= Cv + R
Dividing
(iii) by ndT we
get
(dQndT)p=dQndTv+nRdTndT(dQndT)p=dQndTv+nRdTndT
And
as we know, (dQndT)p=Cp, (dQndT)p=Cp
Similarly,
(dQndT)v=Cv,
(dQndT)v=Cv
Putting
these values, we get,
Cp
= Cv +R
2) Adiabatic processes:-
In contrast to this, consider a gas that is allowed to
slowly escape from a container immersed in a constant-temperature bath. As the
gas expands, it does work on the surroundings and therefore tends to cool, but
the thermal gradient that results causes heat to pass into the gas from the
surroundings to exactly compensate for this change. This is called an isothermal expansion.
In an isothermal process, the internal energy remains constant and we can write
the First Law
0=q+w
q= –w
This illustrates that the heat flow and work done exactly balance each
other.
Because
no thermal insulation is perfect, truly adiabatic processes do not occur.
However, heat flow does take time, so a compression or expansion that occurs
more rapidly than thermal equilibration can be considered adiabatic for
practical purposes. If you have ever used a hand pump to inflate a bicycle
tire, you may have noticed that the bottom of the pump barrel can get quite
warm. Although a small part of this warming may be due to friction, it is
mostly a result of the work you (the surroundings) are doing on the system (the
gas.)
Adiabatic
expansion and contractions are especially important in understanding the
behavior of the atmosphere. Although e. we
commonly think of the atmosphere as homogeneous, it is not, due largely to
uneven heating and cooling over localized areas. Because mixing and heat
transfer between adjoining parcels of air does not occur rapidly, many common
atmospheric phenomena can be considered at least quasi-adiabatic.
3) Isochoric processes:-
a) The work done is given by dW=Pdv.
b) Since in the isochoric process dv=0,
therefore the work done is also zero.
c) From the first law of
thermodynamics, we have,dU=dq+dW.
dU=dq+0
Therefore, dU=dq
Since a gas's temperature changes following its internal energy, a gas
will warm up during adiabatic compression and cool down during adiabatic
expansion.
7. CONCLUSION
From the following
blog, we conclude that the 'First law of thermodynamic' by various researchers
viz. Rudolf Clausis and Max Born state that heat is
a form of energy, and thermodynamic processes are therefore subject to the
principle of conservation of energy. This means that heat energy cannot be
created or destroyed. It can, however, be transferred from one location to
another and converted to and from other forms of energy.
8. REFERANCES
1)
https://www.sciencedirect.com/topics/chemistry/first-law-of-thermodynamics
2) https://en.m.wikipedia.org/wiki/First_law_of_thermodynamics
Fig 1: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/firlaw2.png
Fig 2: https://static.javatpoint.com/chemistry/images/first-law-of-thermodynamics.jpg
Fig 4: https://www.amazon.co.uk/Poster-Corp-Mathematical-Physicist-Lithograph/dp/B078C4Q88T
Fig 6:
https://iupac.org/
Institute and Group details are as follows:-
Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology
(An Autonomous Institute affiliated to Savitribai Phule Pune University formerly University of Pune)
Academic Year:- 2022 – 2023
Department:- Mechanical Engineering
Class:- SEDA
Batch:- 02
Group No.:- 04
Subject:- Thermodynamics
GROUP DETAILS:-
SR. NO. | NAME OF THE STUDENT | ROLL NO. | PRN NO. |
1 | Pooja Rajendra Lahare | 43 | 12220138 |
2 | Lavkesh Jagadish salunke | 44 | 12220211 |
3 | Varad Anand Lomte | 45 | 12220179 |
4 | Yash Balasaheb Mali | 46 | 12220205 |
5 | Nishiraj Nitin Mane | 47 | 12220010 |
6 | Kaustubh Vinod Palande | 54 | 12220132 |
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