Thermodynamics: Laws, Equations & Examples

Thermodynamics implies the study of the relation between heat, work, temperature, and energy. It is a branch of physics that explains how thermal energy is converted into other forms of energy.

• The laws of thermodynamics determine if the system is able to perform useful work in its surroundings. 
• The term was coined by William Thomson in 1749.
• It is used in the field of science and engineering.
• System, Process and Equilibrium are three important terms used in thermodynamics.
• It transfers energy from one place to another.
• The heat is generated by the movement of particles within an object.
• Human body in a crowded room follows the law of thermodynamics.
• Many people closed in a crowded, closed room follows both the first and second laws.
• Heat from the body of individuals is converted into sweat.

Key Terms: Thermodynamics, Law of Thermodynamics, Entropy, Enthalpy, Temperature, Entropy, Energy, Heat, Work, System, Adibatic Process, Isothermal, Isochoric Process, Isobaric Process 

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What is Thermodynamics?

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Thermodynamics is the study of the combined properties of both heat and work, along with its variations in the state. The whole chapter included in NCERT Class 11 Chemistry is based on supporting the transference and transformation of energy from one form to another.

• The measurement of energy has to be around a specific method. 
• It is basically the education of the flow of energy.
• Thermodynamics is a type of macroscopic science which deals with bulk data.
• It is made from a combination of two words named thermo and dynamics.
• The term thermo means heat, and the word dynamics means mechanical motion that requires work.
• The process deals with the interrelation of radiation, energy and physical characteristics of matter.

Thermodynamics Timeline

The timelines used in the field of thermodynamics are as follows:

Thermodynamics Timeline

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Different Branches of Thermodynamics 

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The different branches of thermodynamics are as follows:

Classical Thernodynamics

Classical Thermodynamics is a type of thermodynamics where the change in state of matter is examined using macroscopic methods. It takes into consideration the unit of temperature and pressure.

Statistical Thermodynamics 

Statistical Thermodynamics is a branch of thermodynamics where the behaviour of molecules can be determined by the properties of molecules and how they interact with others.

Chemical Thermodynamics

Chemical thermodynamics is a branch of chemistry that specifies how energy interacts with other chemical processes. Spontaneity is the main goal of this branch of thermodynamics.

Equilibrium Thermodynamics 

Equilibrium Thermodynamics is defined as the way of transforming energy and matter from one state of the environment to another state of the environment.

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Thermodynamics Terms

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Some terms used in thermodynamic are as follows:

System

System refers to the part of universe where required observations are made. The value of the system is either real or imaginary. It is divided into three categories which are as follows:

Open System

When there is the interchange of energy and material taking place with the surroundings, then it is known as an open system.

Closed System

A system is a closed system when there is no interchange of matter but the exchange of energy is likely to happen.

Isolated System

When no interchange of energy or materials takes place with the surroundings it is then known as an isolated system.

Homogeneous System

A system is thought to be homogeneous when every constituent present is in a similar stage and is uniform throughout the system.

Heterogeneous system

A combination is said to be heterogeneous when it contains two or more points and the composition is not uniform.

State of the system

The state of a thermodynamic system is its macroscopic or bulk possessions which can be labeled by state variables:

• Pressure (P)
• Volume (V)
• Temperature (T)
• Amount (n) 

Surroundings

Everything else in the universe excluding the system is called surroundings.

The Universe = System + Surroundings.

Thermodynamics System and Surroundings

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Thermodynamic Process

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The process of thermodynamics is divided into four categories which are as follows:

Isothermal Process

In the isothermal process, temperature residues are the same throughout the procedure.

Adiabatic Process

In the adiabatic process, heat exchanged with surrounds sums to zero.

Isochoric Process

In the isochoric process, volume remnants are the same all over the process.

Isobaric Process

In the isobaric process, pressure remains similar all through the process.

Thermodynamics Process

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Laws of Thermodynamics 

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Thermodynamics consists of four laws which are as follows:

Zeroth Law of Thermodynamics 

Zeroth law of thermodynamics states that if two bodies are places in thermal equilibrium with the third body then first two bodies tends to be in thermal equilibrium with each other.

T_A = T_C and T_B = T_C

then

T_A = T_B

First Law of Thermodynamics

First Law of Thermodynamics states that energy can neither be created nor destroyed but can be transformed from one form to another.

ΔQ = ΔU + ΔW

Where

• ΔQ is the heat given to a thermodynamic system
• ΔW is the Work Done
• ΔU is the Internal Energy

Second Law of Thermodynamics 

The second law of thermodynamics states that entropy always increases in an isolated system. The isolated system will move toward the state of maximum entropy or thermal equilibrium.

• The entropy of universe is continously increasing due to spontaneous processes taking place in it.

ΔS _system + ΔS _surrounding > 0 i.e., ΔS _total > 0

Second Law of Thermodynamics 

Third law of Thermodynamics

Third law of thermodynamics states that when the value of temperature reaches to absolute zero then entropy of the system will become constant. 

Laws of Thermodynamics

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Thermodynamics Properties

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The important properties of thermodynamics are as follows:

Internal Energy

Internal Energy is the amount of each form of energy that a method can possess. In thermodynamics, it is signified by AM which might change, when

• The heat is passed inside or outside of the system
• Work is performed on or by the system
• The matter moves in or leaves the system

Change in Internal Energy by Doing Work

Bringing the change in the internal energy by performing work. The primary state of the system is state A and Temperature being T_A. Internal energy = u_A. On doing a few mechanical works the innovative state is called state B and the temp is T_B.

• It is established to be T_B > T_A
• u_B is the internal energy after the change.

 Δu = up – u_A

Change in Internal Energy by Transfer of Heat

The internal energy of a system can be improved by the transfer of heat from the surroundings to the system without doing work.

Δu = q

• q stands as the heat immersed by the system.
• It can be dignified in terms of temperature difference.
• q is positive when heat is transferred from the surroundings to the system.
• q is negative when heat is transferred from the system to the surroundings.
• When a change of state is performed by doing work and transfer of heat.

Δu = q + w

The first law of thermodynamics states that energy can neither be produced nor be destroyed. The energy of an isolated system is constant. Δu = q + w.

Work (Pressure-volume Work)

Considering a cylinder that comprises one mole of an ideal gas in which a frictionless piston is fitted.

• Total Volume of the gas = V
• Pressure of the gas = P
• external pressure = P_a
• If, P_a > P
• final volume = V_f
• Distance moved by the piston = l
• cross-sectional area of piston = A
• volume change ΔV = l x A = (V_f – V_i)

P = F/A

• F = P x A
• W = F x d. (force x distance)
• P_a x A x [= P_a (-AV)
• W = – P Δ V
• -ve sign is used for work done by the system in case of expansion in volume by convertions.
• If in a system volume expands from V₁ to V₂

W = – \(\int _{v_i}^{v_f}\) P_a dV

Work Completed in Isothermal and Revocable Extension of Ideal Gas

W _rev = – \(\int _{v_i}^{v_f}\) P_ex dV = – \(\int _{v_i}^{v_f}\) (p_in ± dP) dV. Since dP x dV is very small we can write, 

• W _rev = –\(\int _{v_i}^{v_f}\)P_in dV
• For ideal gas PV = nRT

P = \(\frac{nRT}{V}\)

• Therefore, at constant temperature, 
• W _rev = \(\int _{v_i}^{v_f}\) nRT \(\frac{dV}{V}\) = – nRT In \(\frac{V_f}{V_i}\)

– 2.303 nRT log \(\frac{V_f}{V_i}\)

• Work Completed in Isothermal and Revocable Extension of Ideal Gas

   Work does on an ideal gas in a cylinder when it is compressed by a constant external pressure, P_a (in single step) is equal to the shaded area.

Isothermal and Free Expansion of Gas

For the expansion of an ideal gas into a vacuum W = 0

• Since, P_ex = 0 

Δ U = 0, q = 0 

• For isothermal irreversible change

q = – W = P _ex (V_f – V_i)

• For isothermal reversible change

q = – W = nRT In \(\frac{V_f}{V_i}\)

= 2.303 nRT log \(\frac{V_f}{V_i}\)

• For adiabetic change q = 0

Δ U = W _ad

Enthalpy

Enthalpy is known as the total heat content of the system which is equal to the sum of internal energy and pressure-volume work. Accurately, H = U + PV

Change in Enthalpy

Change in enthalpy is the heat engrossed or developed by the system at constant pressure.

ΔH = q_p

• For exothermic reaction (System fails energy to Surroundings),
• ΔH and q_p both are negative.
• For endothermic reaction (System captivates energy from the Surroundings).
• ΔH and q_p both are positive.

Relation between ΔH and Δu.

Let us consider a general reaction A → B and Let H_A be the enthalpy of reactant A and H_S be that of the products.

H_A = U_A + PV_A

• H_B = U_B + PV_B
• ΔH = H_B - H_A
• = (U_B + PV_B) – (U_A + PV_A​)
• ΔH = ΔU + PΔV (H_B - H_A)
• ΔH = ΔU + PΔV
• At constatnt pressure and temperature using ideal gas law, 
• PV_A = n_ART (For reactant A)
• PV_B = n_BRT (For product B)
• Thus, PV_B  – PV_A  = n_BRT – n_ART
• = (n_B – n_A) RT
• PΔV = Δ n _g RT

ΔH = ΔU + Δ n _g RT

Conventions of Thermochemical Equations

Some important conventions of thermochemical equations are as follows:

• The coefficients in a thermochemical equation mention the number of moles of reactants and products.
• The numerical value of Δ_t H^Θ refers to the numberof the moles of substance specified by an equation.
• If a chemical reaction is reversed, the value of Δ_t H^Θ is reversed in sign. 

Hess’s Law of Continuous Heat Summation

Hess’s Law states that total quantity of heat changed or captivated in a reaction is similar whether the reaction takes place in one step or several steps. Let us consider the following reactions:

• C (graphite,s) + O₂ → CO₂
• Δ_t H^Θ = – 393.5 kJ mol ^-1
• CO (g) + \(\frac{1}{2} \) O₂ (g) → CO₂ (g)
• Δ_t H^Θ = – 283.0 kJ mol ^-1
• CO₂ (g) → CO (g) + \(\frac{1}{2} \)O₂ (g)
• Δ_t H^Θ = + 283.0 kJ mol ^-

It is not possible to conclude the Lattice enthalpy of the ionic compound by direct experiment. Therefore, it can be intended by following steps. The diagrams which show the particular stages are called as Born-Haber Cycle.

 

Spontaneity

A process that can take place by itself or has an inclination to take place is called a spontaneous procedure. The spontaneous process need not be immediate. Its actual speed can differ from slow to quite fast.

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Entropy

The entropy is an amount of degree of randomness or disorder of a method. In this process, the substance is slightly in a solid-state while it is supreme in a gaseous state.

• The change in entropy in a spontaneous procedure and is expressed as ΔS
• Mathematically, Change in entropy is represented as:

(ΔS) = S _{final state (product)} – S _{initial state (reactions)}

• For reversible and isothermal process, 
• Change in entropy is represented as:

 ΔS = \(\frac{q_{rev}}{T} = \frac{ \Delta H}{T}\)

• When a system is in equilibrium, ΔS = 0

Gibbs Energy and Spontaneity

A new thermodynamic function, the Gibbs energy or Gibbs function G, can be termed as G = H-TS

ΔG = ΔH – TΔS

• Gibbs energy change = enthalpy change – temperature x entropy change
• ΔG gives a criterion for freedom at continuous pressure and temperature
• If ΔG is negative (< 0) the procedure is spontaneous.
• If ΔG is positive (> 0) the procedure is non-spontaneous.
• Free Energy Change in Reversible Reaction

The criterion for equilibrium are as follows:

• A + B ⇒ C + D is
• Δ _r G = 0
• When all the reactants and products are in standard state, 
• Δ_r G^Θ is related to the equilibrium constant of the reaction as
• 0 = Δ_r G^Θ - RT In K
• Δ_r G^Θ = – RT In K
• Δ_r G^Θ = – 2.303 RT log K
• Δ_r G^Θ = Δ_r H^Θ  – TΔ_r S^Θ

– RT in K

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Things to Remember

• Thermodynamics specifies relationship between heat, temperature, work and energy.
• Enthalpy, Spontaneity and Entropy are important properties of the law of thermodynamics.
• Photosynthesis is one of the important application of the law.
• Thermodynamics Important Questions and Thermodynamic Property Questions are available for practice.
• NCERT Solutions For Class 11 Chemistry Chapter 6: Chemical Thermodynamics are also available where students can practice NCERT problems.