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# Heat and Thermodynamics:

Heat is a type of energy that causes the sensation of being hot. Thermodynamics is the branch of physics concerned with the energy relationships involving heat, mechanical energy, and other forms of energy. The entire formulation of thermodynamics is based on a few fundamental laws that have been established based on human experience with the experimental behaviour of macroscopic aggregates of matter collected over a long period of time.

Gas Laws:

Gases, like solids and liquids, expand when heated. The volume of expansion of a gas is determined not only by its temperature but also by the pressure it is subjected to. Gases have three variables: volume, pressure, and temperature. The third variable is kept constant to study the variation of any two variables. The gas laws describe the interrelationships between these variables.

Boyle’s Law:

The pressure is inversely proportional to the volume at a constant temperature.

P ∝ 1/V

PV = constant

Charles’s Law

The volume of the gas is directly proportional to the absolute temperature at constant pressure.

Lussac’s Law

The pressure of the gas is directly proportional to the absolute temperature at constant volume.

Perfect Gas Equation:

It is the relationship that exists between the pressure, volume, and temperature of a given mass of gas. It is derived from Boyle's and Charle's laws, which a perfect gas obeys. If one mole of gas is used, then,

PV = RT

Here, P is the pressure

V is the volume

R is the universal gas constant

T is the absolute temperature

Methods of Heat Transfer:

Conduction: The transfer of heat from a hotter part of the body to a colder part of the body without the particles moving in between

.

Convection: The heat transmission caused by the actual movement of the medium

Radiation: The process by which heat is transferred from one point to another without the intervention of any material in between.

Thermodynamic Basic Terminology: ## Thermodynamic Equilibrium:

The thermodynamic equilibrium refers to a system that is in thermal, mechanical, and chemical equilibrium.

Thermal equilibrium: A thermodynamic system is said to be in thermal equilibrium if the temperature of all parts of the system is the same as the surrounding temperature.

Mechanical equilibrium: A thermodynamic system is said to be in mechanical equilibrium if no unbalanced force acts on any part of it or the entire system.

Chemical equilibrium: When a system's chemical composition is the same throughout the system, it is said to be in chemical equilibrium.

## Internal Energy:

Internal energy is the sum of the kinetic and potential energy of atoms/molecules as a result of internal factors. Kinetic energy is the energy that atoms or molecules possess as a result of their motion.

## Zeroth Law of Thermodynamics:

According to the law, "two systems that are in thermal equilibrium with a third system are also in thermal equilibrium with each other."

## Modes of Energy Transfer:

Heat and Work are the two methods for changing the system's internal energy.

Heat: The energy transferred due to the temperature difference between the system and the surrounding area is referred to as heat. When heated, the kinetic energy of the molecules increases, and thus the internal energy.

Work: is defined as the energy expended to overcome an external force. When the system works against external pressure, it tends to reduce internal energy, whereas when the system contracts as a result of external pressure, it tends to increase internal energy.

Thermoelectric Conductivity:

Thermal conductivity refers to a conductor's ability to conduct heat. When the temperature difference between the two faces is 1K, it is defined as the amount of heat flowing per second through the unit area of the block of unit thickness.

Thermodynamics First Law:

If some heat is supplied to a system capable of performing external work, the amount of heat absorbed by the system equals the sum of the system's internal energy increase and the external work performed by the system.

dQ = dU + dW

Here, dQ is the amount of heat given to the system

dU is the increase in the internal energy

dW is the external energy done by the system

Applications of First Law of Thermodynamics:

1. Isothermal Process

3. Isobaric Process

4. Isochoric Process

Work done in an Isothermal Process:

The work done by an ideal gas when it expands isothermally from volume V1 to volume V2 at temperature T is given by

W = RTloge(V2/V1) (for one mole of the gas)

Also W = RTloge(P2/P1) (Since P1V1 = P2V2)

Some of examples of isothermal processes are

1. Melting

2. Boiling

Adiabatic Process Work: Work done by an ideal gas in an adiabatic process is given by T1 and T2 are the temperatures of the gas in its initial and final states.

Some illustrations of the adiabatic process:

• Sound wave propagation in a gas

• The rupture of an air-inflated automobile tube

Work carried out in an Isobaric Process:

• W = P gives the work done in an isobaric process (V2 – V1)

• An isobaric process is the heating of water or any liquid at atmospheric pressure.

Work completed through an Isochoric Process:

• W = 0 for work done in an isochoric process.

• The process of converting a solid into a liquid is nearly isochoric because the change in volume due to melting is negligible.

(a) For an isothermal process

Q = nRTloge (V2/V1)

Q = 0

(c) For isobaric process

Q = nCp△T

(d) For the isochoric process

Q = nCv△T

Thermodynamic First Law Limitations:

1. The first law of thermodynamics does not specify the possible direction of change.

2. The law does not specify the extent to which the change can occur.

Heat Capacity Specific:

The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of the substance's unit mass by 10 degrees Celsius.

(a) Specific Heat Capacity at Constant Volume: The specific heat capacity at constant volume is the amount of heat required to raise the temperature of one gas by ten degrees Celsius while keeping the volume constant.

(b) Constant Pressure Specific Heat Capacity:

The specific heat capacity at constant pressure is the amount of heat required to raise the temperature of 1 gramme of substance by 10 degrees Celsius while keeping the pressure constant.

The Mayer Formula:

The difference between a gas's specific heat at constant pressure and its specific heat capacity at constant volume is given by Mayer's formula. Mayer's formula is written as

Cp – Cv = R

Here, Cp is the specific heat capacity at constant pressure.

Cv is the specific heat capacity at constant volume

R is the universal gas constant

Mayer’s relation is valid only for perfect gases

Latent Energy:

The amount of heat required to change the state of a substance's unit mass at constant pressure and temperature is referred to as latent heat.

L = ΔQ/m

• The amount of heat required to change a solid into a liquid is known as the latent heat of fusion.

• The latent heat of vaporization is the amount of heat required to convert a liquid to a gas.

Newton Law of Cooling:

If the temperature difference between the body and its surroundings is small, the rate of heat loss by the body is directly proportional to the difference.

Degrees of Freedom:

The total number of independent variables required to specify the position of the object is referred to as the degrees of freedom.

Law of Equipartition of Energy:

According to the law of energy equipartition, the total energy is equally shared by all degrees of freedom, and the average energy of a molecule in a gas associated with each degree of freedom is (12) kT.

The Boltzman constant is denoted by k, and the absolute temperature is denoted by T.

Ratio of specific heats:

An important constant is the ratio of a gas's specific heat capacity at constant pressure to that at constant volume (Cp/Cv). It has a value between 1 and 1.67

The knowledge of helps in finding the atomicity of gas as well as the molecular structure of the gas

## Second Law of Thermodynamics:

Kelvin- Planck’s Statement:

It is impossible to generate a steady supply of work by cooling a body to a temperature lower than the coolest of its surroundings.

Clausius Proposition:

It is impossible to transfer heat from a lower temperature body to a higher temperature body without performing external work on the working substance.

Heat Generator:

A heat engine is a machine that converts mechanical energy from heat energy. The heat engine is made up of three parts: the hot body known as the source, the working substance, and the cold body known as the sink. A cyclic process is used to obtain the working substance. During the process, the working substance will absorb heat from a higher-temperature source and perform some work. Efficiency of the Heat Engine:

The thermal efficiency of a heat engine is the ratio of the heat converted into work to the total heat absorbed from the source over the course of a complete cycle. During isothermal expansion, the working substance absorbs a certain amount of heat Q1. During isothermal compression, it rejects a certain amount of heat Q2 into the sink.

Efficiency, η = Work done/heat supplied

= (Q1 – Q2)/Q1

= 1 – Q2/Q1

Q2/Q1 = T2/T1

η = 1 – T2/T1

The efficiency of Carnot's engine is solely determined by the temperature of the source and sink. It will not be affected by the working substance.

Enthalpy:

Because chemical reactions are typically carried out at constant pressure (atmospheric pressure), the new state function Enthalpy has been discovered to be useful. The sum of a thermodynamic system's internal energy and the product of its pressure and volume yields enthalpy. Because it has the dimension of energy, it is measured in joules or ergs.

H = U + PV

Here, H is the enthalpy

U is the internal energy

P is the pressure

V is the volume

Factors Affecting the Enthalpy of a Reaction:

a) Temperature

b) Physical states of reactants and products

c) Allotropic forms of elements

d) Pressure and Volume

Entropy

Entropy is the amount of thermal energy per unit temperature that is not available for useful work. The ordered movement of molecules will produce useful work. Entropy is the amount of molecular disorder or randomness in the system.

Important Entropy Facts :

a) Natural processes increase the universe's entropy.

b) Change in entropy is solely determined by the system's initial and final states

c) No entropy is conserved

d) Entropy can be created, but it cannot be destroyed.

Clausius Clapeyron Equation:

It relates the rate of pressure change with temperature to latent heat. It can be used to describe any equilibrium between two phases, such as solid and liquid, liquid and water, and so on. The Clausius Clapeyron Equation states that Here, L is the latent heat

V1 is the volume of the first state

V2 is the volume in the final state into which the substance changes

Latent heat is the quantity of heat supplied to the unit mass of the substance during the change of state

Liquid-Vapour Equilibrium- Boiling Point:

The boiling point temperature is the temperature at which the substance's liquid and vapour phases coexist in equilibrium. The Clapeyron equation can be written for this equilibrium as Here,

The molar volumes of the vapour and liquid phases are denoted by Vv and Vl, respectively.

• T is the substance's boiling point.

• Hv is the substance's molar latent heat of vaporisation.

• The rate of change of boiling point with pressure is given by dT/dP.

• The volume Vv of a substance's vapour phase of a given mass is always much greater than the volume Vv of the same substance's liquid phase. As a result, dT/dP is always positive.

Carnot Engine:

Carnot's theoretical thermodynamic cycle, proposed in 1824, is known as the Carnot Engine. He used a heat engine to perform a cyclic process that was completely reversible. There is no engine that can be more efficient than a Carnot reversible engine operating between a source and a sink at two given temperatures. This is referred to as Carnot's principle.

In a Carnot's engine, the working substance goes through a reversible cycle of operations that includes two isothermal and two adiabatic processes. Refrigerator:

It is a device used to keep bodies at a lower temperature than the surrounding environment.

Performance coefficient:

The amount of heat removed per unit of work done is referred to as a refrigerator's coefficient of performance.

## Gibbs free energy (G):

The Gibbs free energy is defined as a new thermodynamic state function G.

G = H + TS or G = H + TS (at constant temperature and pressure)

G must be negative for a spontaneous reaction to occur. The use of Gibbs free energy has the advantage of referring only to the system.

Third Law of Thermodynamics:

According to the third law of thermodynamics, "At absolute zero, the entropy of a perfectly crystalline substance is taken as zero," which means that at absolute zero, every crystalline solid is in perfect order and its entropy should be zero. At room temperature, the absolute value of entropy for a pure substance can be calculated using the third law.

Important Point to remember:

• Thermodynamics studies the energy relationships between heat, mechanical energy, and other types of energy.

• Internal energy is the sum of the system's total kinetic and potential energy.

• The zeroth law of thermodynamics explains the concept of temperature.

• The first law of thermodynamics describes the relationship between heat transferred, work done, and internal energy change.

• The isothermal process, adiabatic process, isobaric process, and isochoric process are examples of thermodynamic processes.

• The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of the substance's unit mass by 10 degrees Celsius.

• Kelvin-Planck and Clausius stated the second law of thermodynamics.

• A heat engine is a mechanical device that converts heat energy into mechanical energy.

• The sum of a thermodynamic system's internal energy and the product of its pressure and volume yields enthalpy.

• Entropy is the amount of thermal energy per unit temperature that is not available for useful work.

• The amount of heat removed per unit of work done is referred to as a refrigerator's coefficient of performance.

• According to the third law of thermodynamics, "at absolute zero, the entropy of a perfectly crystalline substance is taken to be zero."