## What is Thermodynamics?

The word thermodynamics consists of two words: thermo- and dynamics. Dynamics means the study of motion. The field of thermodynamics is all about the study of the movement of heat. In a more meaningful way, it is stated as the study of the transfer of energy. Energy transfer is something that we encounter in day-to-day life. Automobiles, chemical reactions, refrigerators, and power generators work on the basis of thermodynamic principles.

## System and Surrounding

In thermodynamics, the entire universe is composed of two components i.e. system and surrounding. The system is the component in which observations are made. A beaker of water is an example of a system. We can measure the quantities like temperature, volume, and mass. The region outside the beaker is the surrounding. The beaker acts as the boundary between the system and the surroundings.

The three kinds of thermodynamic systems are:

### Open system

Any system is an open system if both energy and matter are exchanged with the surrounding. Boiling water in a container without a lid is an open system. When the water in an open container is boiled. The vapor escapes to the surroundings and also the energy is supplied as heat energy to the system from an external source of energy.

### Closed system

The system becomes a closed system if the boiling water is sealed with a lid so that no water vapor can escape while heat energy is given to the system. The transfer of energy can be allowed in the closed system. But the exchange of matter is not allowed.

### Isolated system

If the water is placed in the completely sealed container of thermally insulating material. Then, energy and matter are never exchanged between the surroundings, this system is termed an isolated system.

In thermodynamics, we study about the movement of energy from the system and the surrounding and vice versa. The system may undergo several changes during the movement of energy. Hence, it is relevant to completely observe the system while the energy is exchanged. When the water in a container is boiled by supplying heat, the quantities like temperature, pressure, and volume of water change. These quantities are called state variables or state functions. These parameters are required to describe the thermodynamic state of the system.

The internal energy of any system is a prominent state variable. Internal energy is the energy stored within the thermodynamic system. This external macroscopic factor does not affect internal energy but depends upon the thermodynamic state of that system. Consider a beaker of water, if the beaker is at rest then the external kinetic energy of this system is zero. But the water molecules undergo transition, vibration, and rotation. The molecules are bound to each other with chemical bonds. These microscopic factors affect internal energy.

Internal energy that is stored in a system may be altered during some thermodynamic process. If a thermodynamic system is heated by supplying heat energy, the internal energy raises. In some cases, internal energy is liberated as other forms of energy. When fuels like petrol or methane are ignited, the chemical energy stored within the system is liberated as heat energy.

In thermodynamics, measuring internal energy is irrelevant, we are rather interested in changes in internal energy.

Internal energy can also alter if work is done on or by the system. If a container of adiabatic walls filled with water is stirred vigorously, temperature of water rises. The temperature is a prominent state variable. Hence, whenever the temperature of the system changes, also internal energy changes.

The change in internal energy is denoted by △U (in joules).

## Statement of the first law of thermodynamics

The internal energy of a closed system can be altered by either supplying heat or doing work. No other factors can affect internal energy. The first law of thermodynamics is expressed using the following equation,

$△U=Q+W$

Where,

Q is heat energy transferred (in joules).

W is work done on the system (in joules).

If work is done by the system, then the equation becomes,

$△U=Q-W$

When energy is transferred to any system, the energy transferred is either stored as internal energy or is spent to do some work. Any fraction of the transferred energy does not vanish. The first law of thermodynamics also says that energy cannot appear from anywhere but it is always changed from one kind to another. The first law of thermodynamics is also referred to as the law of conservation of energy. The first law of thermodynamics also stated as the net energy of the universe is constant.

## The thermodynamics of a closed system

Let us apply the first law to a closed system as the thermodynamics of a closed system is easy to understand. Only transfer of energy is allowed hence, it is one the simplest systems to understand thermodynamics. Consider a cylinder filled with gas. When the gas expands, work is done by the system. Since, the temperature of this system remains constant, this process is called the isothermal process. Since, temperature does not change during this process, the net internal energy of the closed system remains the same too.

Hence, for an isothermal process,

$∆U=0$

From the first law, we obtain the following equation,

$0=Q-W$

$Q=W$

In this process, the supplied heat is converted to mechanical work, the equation for heat energy is obtained as,

$Q=P∆V$

Where  ∆V is the net volume change.

## Heat engine

Heat engines are best explained using the first law of thermodynamics. Heat engine transforms heat energy into mechanical energy. A steam engine is a simple kind of heat engine. In a steam engine, the water is converted to steam say from lower temperature T1 to higher temperature T2. The steam with high pressure is used to push the piston of the steam engine. Let Q1 be the heat energy given to the steam initially. The engine absorbs some parts of energy to perform mechanical work however, some fraction of heat energy Q2 is liberated to the surrounding. If the temperature of the steam falls back to T1 again then from the first law, the equation becomes,

$∆U=0$

$W={Q}_{1}-{Q}_{2}$

The fraction of energy consumed by the engine is given using the following equation,

$\eta =\frac{W}{{Q}_{1}}$

$\eta =\frac{{Q}_{1}-{Q}_{2}}{{Q}_{1}}$

$\eta =1-\frac{{Q}_{2}}{{Q}_{1}}$

Where η is the efficiency of the heat engine.

$\eta =1$ if the heat escaped to the surrounding ${Q}_{2}=0$, which means the efficiency is maximum.

Note: In the above example, the steam engine returns to its initial state each time the heat is released. This process is referred to as a cyclic process. In the cyclic process net change in internal energy is zero.

The second law is used to study the thermodynamic process in more detail. The first law is all about the conservation of energy while the second law deals with the enthalpy and entropy of the system.

## Formulas

The formula to find the change in internal energy is,

$∆U=Q+W$

Where,

∆U is the change in internal energy (in joules).

Q is the heat transferred (in joules).

W is the total work done.

The efficiency η of a typical heat engine is given as,

$\eta =1-\frac{{Q}_{2}}{{Q}_{1}}$

Where,

${Q}_{1}$ is the quantity of heat energy given to the engine (in joules).

${Q}_{2}$ is the quantity of heat released into the surrounding (in joules).

## Context and Applications

This topic is significant in physics for both undergraduate and graduate courses, especially for bachelors and masters in science, and bachelors in technology.

## Practice Problems

Question 1: A heat engine, which undergoes a cyclic process liberates 500 J of heat energy. If the efficiency of the heat engine is 60%. What is the quantity of heat supplied to the engine while combustion of fuel?

(a) 1250 J

(b) 3256 J

(c) 1345 J

(d) 723 J

Answer: The correct option is (a).

Given data

$\eta =60%=\frac{60}{100}=0.6$

${Q}_{1}=?$

Explanation:

$\eta =1-\frac{{Q}_{2}}{{Q}_{1}}$

$\frac{{Q}_{2}}{{Q}_{1}}=1-\eta$

${Q}_{1}=\frac{{Q}_{2}}{1-\eta }$

$Q1=\frac{500}{1-0.6}=\frac{500}{0.4}$

Hence, the quantity of supplied energy to the engine is (a)

Question 2: According to thermodynamics, which of the following is conserved?

(a) Total energy

(b) Mass

(c) Kinetic energy

(d) Temperature

Answer: The correct option is (a).

Explanation: According to the first law of thermodynamics, the total energy of the universe is conserved. The energy is always converted from one state to another.

Question 3: The efficiency of an engine is 100 percent. What does it mean?

(a) The total energy is conserved

(b) No energy is lost to the surroundings

(c) Energy is completely lost

(d) No work is done by the engine

Answer: The correct option is (b).

Explanation: When the efficiency of an engine is 100 percent then the amount of energy supplied is the same as the work done by the system. Hence there is no energy loss.

Question 4: The temperature of a system is also the measure of _____.

(a) Change in internal energy

(b) Change in kinetic energy

(c) Change in pressure

(d) Energy stored in the system

Answer: The correct option is (a).

Explanation: Change in internal energy in any system is related to the temperature of the system. The temperature of a system depends upon the state of the system. Internal energy indicates the state of the system.

Question 5: For an isothermal process, the change in internal energy is ____.

(a) Positive

(b) Negative

(c) Zero

(d) None of the above

Answer: The correct option is (c).

Explanation: For an isothermal process the temperature remains constant. The heat supplied is completely spent to do work on the system. Hence, from the first law, the change in internal energy is zero.

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