Thermodynamics - Topics, Formulas, Tips, Books, FAQs

Important Topics of Thermodynamics

The significant concepts of the chapter Thermodynamics describe the ways energy can be exchanged in terms of heat and work and influence the state of a system. These topics bring in the laws of thermal equilibrium, energy conservation and the direction of natural processes. Knowing them will enable one to understand how engines, refrigerators and lots of natural phenomena work. These topics are crucial in developing an effective grounding in terms of thermal physics.

1. Thermodynamic System and Surroundings

A given portion of the universe that is selected to be studied is a thermodynamic system, and the rest, which make up the surroundings, are referred to as the surroundings. The exchange of mass and energy can be used to classify systems into the open, closed and isolated. A proper definition of the system assists in the proper analysis of energy transfer. This is the concept of all thermodynamic analysis. It is necessary to apply the laws of thermodynamics properly.

2. Thermodynamic Variables and State of a System

A thermodynamic state of a system is described by measurable state variables like pressure (P), volume (V), temperature (T), and mass.

These variables define the macroscopic condition of the system.
When the system changes from one state to another, these variables also change.
For an ideal gas, the relation among the state variables is given by the Equation of State:

$
P V=n R T
$

State variables are concerned only with the present state of the system, but not with the path that the system followed to arrive at a specific state. This concept assists in differentiating between path and state-dependent quantities. It is very important in the study of thermodynamic processes.

3. Thermal Equilibrium and Zeroth Law of Thermodynamics

Thermal equilibrium is a term used to refer to the inability of two systems in contact to exchange heat. The zeroth law holds that when two systems are in thermal equilibrium with some third system, then they are in thermal equilibrium with one another. This law furnishes a standard of measurement of temperature. It defines temperature as a basic and quantifiable value. The zeroth law facilitates uniformity of temperature scales.

4. Heat and Work

Two ways of energy transfer between a system and its surroundings are heat and work. Heat transfer takes place because of the difference in temperature, and work transfer because of the macroscopic forces. Heat and work are dependent on the route that is taken in a process. They are not properties of the system but describe energy in transit. To use the first law of thermodynamics, it is necessary to understand heat and work.

Heat (Q): The energy transferred because of the temperature difference between the system and its surroundings. It flows from the hot to the cold body.

Work (W): The energy transferred when a force is applied, and displacement occurs (e.g., expansion or compression of a gas).

5. First Law of Thermodynamics

The first law is the law of conservation of energy applied to a thermodynamic system. It states that: "Energy can neither be created nor destroyed, it can only change from one form to another."

In thermodynamics, the change in internal energy of a system $(\boldsymbol{\Delta} \mathbf{U})$ is equal to the heat supplied to the system (Q) minus the work done by the system (W):

$
\Delta U=Q-W
$

6. Internal Energy

The total microscopic energy of a system as a result of the movement and interactions of molecules in the system is known as internal energy. It contains the kinetic energies and the potential energies at the molecular scale. Internal energy is dependent on the system only. Alterations in internal energy are a result of heat exchange or work. This principle aids in explaining the changes in temperatures and the storage of energy in the systems.

7. Thermodynamic Processes

A path through which a system can change state to another one is known as a thermodynamic process. Widely known processes are isothermal, adiabatic, isobaric and isochoric. The different processes possess unique features in terms of heat and work exchange. Knowledge of these processes makes problem-solving simple. They are often applied in conceptual and numerical questions.

8. Second Law of Thermodynamics

The second law describes the natural course of the thermodynamic processes. According to it, without any work, a body can not allow heat to flow spontaneously to a hot body when it is colder than that body. This law brings about the notion of irreversibility. It gives the reason why some of the processes are irreversible. The second law is the basis of the interpretation of heat engines and refrigerators.

• Kelvin-Planck Statement: It is impossible to construct a heat engine that converts all the absorbed heat into work without rejecting some heat to a sink.
• Clausius Statement: Heat cannot flow on its own from a colder body to a hotter body.

10. Carnot Engine

The Carnot engine is an ideal heat engine proposed by Sadi Carnot. It works between two temperature reservoirs and gives the maximum possible efficiency for a heat engine.
Working principle: It operates on the Carnot cycle, which consists of four reversible processes:
1. Isothermal expansion
2. Adiabatic expansion
3. Isothermal compression
4. Adiabatic compression
Efficiency of Carnot engine: $\eta=1-\frac{T_2}{T_1}$

Related topics,

Important Formulas of Thermodynamics

The chapter Thermodynamics contains formulas that describe quantitative relations of the following terms in different thermodynamic processes: heat, work, internal energy and temperature. These relations are important in solving numerical problems and the mechanics of heat engines, refrigerators, and thermal systems.

1. Zeroth Law of Thermodynamics:

• If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

2. First Law of Thermodynamics:

$
\Delta U=Q-W
$

where
$\Delta U=$ change in internal energy,
$Q=$ heat supplied to the system,
$W$ = work done by the system.

3. Work Done in Thermodynamic Processes:

$W=\int P d V$

4. Isothermal Process (Constant Temperature):

• Change in internal energy:

$
\Delta U=0
$

• Work done:

$
W=n R T \ln \left(\frac{V_2}{V_1}\right)
$

5. Adiabatic Process (No Heat Exchange):

• Heat exchanged:

$
Q=0
$

• Relation between temperature and volume:

$
T V^{\gamma-1}=\mathrm{constant}
$

• Relation between pressure and volume:

$
P V^\gamma=\mathrm{constant}
$

6. Isobaric Process (Constant Pressure):

• Work done:

$
W=P\left(V_2-V_1\right)
$

• Heat supplied:

$
Q=n C_p \Delta T
$

7. Isochoric Process (Constant Volume):

• Work done:

$
W=0
$

• Heat supplied:

$
Q=n C_v \Delta T
$

8. Relation between Heat Capacities:

• Mayer's Formula

$
C_p-C_v=R
$

• Ratio of heat capacities:

$
\gamma=\frac{C_p}{C_v}
$

9. Internal Energy of an Ideal Gas:

$
U=\frac{f}{2} n R T
$

where $f=$ degrees of freedom.

10. Efficiency of a Heat Engine:

$\eta=\frac{W}{Q_H}$

11. Carnot Engine Efficiency:

$\eta=1-\frac{T_C}{T_H}$

Thermodynamics: Previous Year Questions

Past year questions of the chapter Thermodynamics are primarily aimed at the application of the zeroth, first, and second laws of thermodynamics, thermodynamic processes, and heat engines. These questions will make students aware of the exam pattern, and they will know which concepts and formulas are mostly tested. Their practice enhances the ability to define concepts and solve numerical problems. This part is very helpful in effective revision and examination-oriented preparation.

Question 1:

An ideal gas is taken via the path as shown in the figure. The net work done in the whole cycle is

Solution:

Work done is the area enclosed.

$
\begin{aligned}
& W \text { ork done }=\frac{1}{2}\left(3 V_1-V_1\right)\left(4 P_1-P_1\right) \\
& W=-3 P_1 V_1
\end{aligned}
$

Question 2:

When 30J of work was done on the gas, 20J of heat energy was released. If the initial energy of the gas was 40J, what is the final internal energy (In J)?

Solution:

$
\Delta U=Q-W=(-20)-(-30)=10 J
$

$\Delta U$ is positive, so internal energy is increasing.

$
\begin{aligned}
& \Delta U=U_f-U_i=10 \Rightarrow U_f-40=10 \\
& U_f=50 J
\end{aligned}
$

Question 3:

One mole of an ideal monoatomic gas undergoes a process described by the equation $P V^3=$ constant. The heat capacity (in terms of R ) of the gas during this process is

Solution:

$
P V^3=C(N=3)
$
Specific heat in a polytropic process

$
\begin{aligned}
& P V^N=K \\
& C=C_V+\frac{R}{1-N} \\
& =\frac{3}{2} R+\frac{R}{1-3} \\
& =\frac{3}{2} R-\frac{R}{2}=R
\end{aligned}
$

Thermodynamics in Different Exams

Thermodynamics is an essential and scoring chapter in most of the level school-level and competitive exams because of its firm conceptual foundation and numerical activities. This chapter is examined by different tests that include questions about the thermodynamic laws, processes, heat engines, and refrigerators. The clarity of concepts, assumptions, and formulae will allow the students to cope with a wide range of questions of different problems.

Important Books and Resources for Class 11 Thermodynamics

To master the chapter Thermodynamics, students should refer to reliable textbooks, reference books, and practice materials that clearly explain thermodynamic laws, processes, and applications, such as heat engines and refrigerators. These resources help build strong conceptual clarity and numerical problem-solving skills required for school exams and competitive exams like JEE Main, JEE Advanced, and NEET.

NCERT Resources for Thermodynamics

The NCERT material on the chapter Thermodynamics gives a clear and exam-oriented form of understanding of the laws of heat, work, and transfer of energy. Concepts like thermodynamic systems, laws of thermodynamics, processes, and heat engines are introduced at a simple level, which is presented by the NCERT textbook and exemplar problems through diagrams and solved examples. Proper study of the NCERT contributes to the development of good conceptual knowledge and numerical solving skills. Such resources are the basis of board exams in Class 11 and even competition exams such as JEE Main and NEET.

• NCERT solutions for Class 11 Physics Chapter 11 Thermodynamics
• NCERT notes Class 11 Physics Chapter 11 Thermodynamics
• NCERT Exemplar Class 11 Physics Solutions Chapter 12