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First Law Of Thermodynamics, Process, Internal Energy, Examples, Important Topics For JEE 2025
First Law Of Thermodynamics : Explore the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed. Understand its implications in energy conservation, internal energy changes, and heat-work interactions in thermodynamic systems.
Shrivastav 9 Jun, 2024
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First Law Of Thermodynamics In Physics
Thermodynamics In Physics :
Thermodynamics is the study of the relations between heat, work, temperature, and energy. Thermodynamics is concerned with the work done by a system and the heat it exchanges with its surroundings. Alternatively, it is the study of changes that occur in some part of the universe (we designate as the system) and then everything else (outside the system) is the surrounding.
A real or imagined boundary may separate the system from its surroundings. A collection of properties such as pressure, volume, temperature and some other properties to be discussed later characterize the thermodynamical state of a system. The laws of thermodynamics describe how the energy in a system changes and whether the system can perform any useful work on its surroundings.
Thermodynamic Process
Thermodynamic Process :
Thermodynamics basically deals with the exchange of heat between a body and the surrounding along with the other processes accompanying it, such as the work involved and the changes in the internal energy, taking place in the body. Such studies are primarily carried out in terms of a few macroscopic properties, such as pressure, volume, temperature, etc.
Any alteration in one or more of the macroscopic properties of a body renders specific changes in other related properties, and the body is said to have been subjected to a thermodynamic process (or is said to have undergone a thermodynamic process).
The body which is subjected to a thermodynamic process is known as a thermodynamic system. The macroscopic parameters in terms of which the study of a thermodynamic process is carried out are known as thermodynamic variables. For example, gas enclosed in a cylinder fitted with a piston forms the thermodynamic system but the atmospheric air around the cylinder, movable piston, burner, etc., is the surrounding.
The process of change of state of a system involves change of thermodynamic variables such as pressure P, volume V and temperature T of the system. During such a process, energy may be transferred into the system from the thermal reservoir (positive heat) or vice versa (negative heat). The process is known as thermodynamic process. Some important processes are:
Isothermal process: Temperature remain constant
Adiabatic process :
No transfer of heat Isobaric process: Pressure remains constant
Cyclic and non-cyclic processes :
In cyclic process, initial and final states are same while in non-cyclic process these states are different.
Internal Energy In thermodynamics
Internal energy is one of the most important concepts in thermodynamics. When we discuss energy changes for an object sliding with friction, we stated that warming an object increased its internal energy and that cooling the object decreased its internal energy. But what is internal energy? We can look at it in various ways; let’s start with one based on the ideas of mechanics. Matter consists of atoms and molecules, and these are made up of particles having kinetic and potential energies. We tentatively define the internal energy of a system as the sum of the kinetic energies of all of its constituent particles, plus the sum of all the potential energies of interaction among these particles.
We use the symbol U for internal energy. (We used this symbol in our study of mechanics to represent potential energy. However, U has a different meaning in thermodynamics.) During a change of state of the system, the internal energy may change from an initial value U
1
to a final value U
2
. We denote the change in internal energy as ∆U = U
2
– U
1
.
First Law Of Thermodynamics
Consider a system that consists of a gas enclosed by a piston in a cylinder. Suppose the system is taken quasistatically from an initial state Pi, Vi, Ti to a final state Pf, Vf, Tf. At each step the work done and heat exchanged are measured. We know that both the total work done W and the total heat transfer Q to or from the system depend on the thermodynamic path. However, the difference Q – W is the same for all paths between the given initial and final equilibrium states, and it is equal to the change in internal energy ΔU of the system.
ΔU = Q – W
In the above statement, Q is positive when heat enters the system and W is positive when work is done by the system on its surroundings. The equation, is the mathematical statement of the First Law of Thermodynamics. It states that the internal energy of a system changes when work is done on the system (or by it), and when it exchanges heat with the environment.
Note that the First Law is valid for all processes, quasistatic or not. However, if friction is present, or the process is not quasi static, the internal energy U is uniquely defined only at the initial and final equilibrium states. The First Law establishes the existence of internal energy U as a state function–one that depends only on the thermodynamic state of the system.
In the macroscopic approach of thermodynamics, there is no need to specify the physical nature of the internal energy. The experimental results are sufficient to prove that such a function exists. The internal energy is the sum of all possible kinds of energies stored in the system–mechanical, electrical, magnetic, chemical, nuclear, and so on. It does not include the kinetic and potential energies associated with the centre of mass of the system.
Basically, When the Law of Conservation of Energy was first introduced it was stated that the mechanical energy (kinetic + potential) of a system is conserved in the absence of non-conservative forces such as friction. That is, the changes in the internal energy of the system were not included in this mechanical model.
Right Sign Conventions Should Be Followed While Using The First Law Of Thermodynamics
Heat gained by the system is positive
Heat lost by the system is negative
Gain in internal energy is positive
Loss in internal energy is negative
Work done by the system is positive (i.e., during expansion)
Work done on the system is negative (i.e., during compression)
Examples Of First Law Of Thermodynamics
Q.1.
A gas is taken from state-1 to state-2 along the path shown in figure.
If 70 cal of heat is extracted from the gas in the process, calculate the change in internal energy of the system.
Ans.
Since work done is equal to the area under the
P-V
graph, so in this case work done will be the negative shaded area as shown in Figure. Negative because volume is decreasing
Since, 70 cal of heat is extracted in the process, so
Q
= –70 cal = 70 × 4.2 J = –294 J
From First Law of Thermodynamics (FLTD), we get
Hence, the internal energy of gas decreases by 241.5 J in the given process.
2.
A sample of an ideal gas is taken through the cyclic process abca (figure ). It absorbs 50 J of heat during the part ab, no heat during bc and rejects 70 J of heat during ca. 40 J of work is done on the gas during the part bc. (a) Find the internal energy of the gas at b and c if it is 1500 J at a. (b) Calculate the work done by the gas during the part ca.
Ans.
(a)
In the part
ab
the volume remains constant. Thus, the work done by the gas is zero. The heat absorbed by the gas is 50 J. The increases in internal energy from
a
to
b
is
As the internal energy is 1500 J at
a
, it will be 1550 J at
b
. In the part
bc
, the work done by the gas is
and no heat is given to the system. The increase n internal energy from
b
to
c
is
As the internal energy is 1550 J at
b
, it will be 1590 J at
c
.
(b)
The change in internal energy from
c
to
a
is
The heat given to the system is
Using
3.
Heat taken from a gas in a process is 80 J and increase in internal energy of the gas is 20 J. Find work done by the gas in the given process.
Ans.
Heat is taken from the gas. Therefore,
Q
is negative. Or,
Q
= –80 J
Internal energy of the gas is increasing
Therefore,
is positive. Or
Using the first law equation,
Here, negative sign indicates that volume of the gas is decreasing and work is done on the gas.
4.
The temperature of
n
-moles of an ideal gas is increased from
T
0
to 2
T
0
through a process
Find work done in this process.
Ans.
pV
=
nRT
(ideal gas equation)
…(i)
And
…(ii)
Dividing Eq. (i) by Eq. (ii), we get
= 2
nRT
0
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