# Thermodynamics

MCQs**System and Surrounding**

The part of universe which is under study is called system and the rest part of the universe is called surrounding. That means the universe is the combination of system and surrounding.

**Types of System**

**Open System**

The system which can exchange both heat and matter with the surrounding is called open system. Hot water in a beaker is an example of this system.

**Closed System**

The system which can exchange only heat but not matter with the surrounding is called closed system. Hot water in a sealed tube is an example of this system.

**Isolated System**

The system which can exchange neither energy nor matter with the surrounding is called Isolated system. Hot water in a thermos flask is an example of this system.

**Thermodynamic Process**

When a system changes itself from one to another state, the operation is called procss.

**Isothermal Process**

The process which takes place at constant temperature is called isothermal process.

i.e. ΔT=O

**Adiabatic Process**

The process in which no heat change occurs is called adiabatic process.

i.e. ΔQ=O

**Isochoric Process**

The process which takes place at constant volume is called isochoric process.

i.e. ΔV=O

**Isobaric Process**

The process which takes place at constant pressure is called isobaric process.

i.e. ΔP=O

**Cyclic Process**

When a system undergoes a number of different processes and finally returns to its initial state, it is termed as cyclic process.

In cyclic process change in all state function will be zero. i.e. ΔE = 0, ΔH = 0, ΔP = 0, ΔT = 0

**Reversible Process**

The process which takes place infinitesimally slowly and whose direction at any point can be reversed by applying an infinitesimal change in the state of the system is called reversible Process. It is an ideal process. Work obtained in expansion is maximum and system is in virtual equilibrium at any state.

**Irreversible Process**

The process which takes place in one step and can not be reversed. This is a fast process. All natural processes are irreversible and system is in equilibrium only at initial and final state.

**Spontaneous Process and Nonspontaneous Process**

The process which proceeds of its own accord without any outside assistance or help is called Spontaneous Process or Natural Process and the reverse process which does not proceed on its own accord is called nonspontaneous process.

Spontaneous process is unidirectional, for reverse change work has to be done. For spontaneous process time is no factor. It may takes palce rapidly or very slowly. If a system is not in equilibrium state, a spontaneous change is inevitable. The change will continue untill equilibrium exist. Once the system attains the equilibrium it does not undergo further spontaneous change. Spontaneous process or change is accompanied by decrease of internal energy of enthalpy.

The tendency of a process to occur naturally is called Spontaniety.

Examples

A rolling ball down the hill spontaneously but it will not rall uphill unless work is done on it.

When two metal ball one hot and one cold are connected to each other, the heat flow from hotter to colder ball spontaneously but can never from colder to hotter ball spontaneously.

**Extensive and Intensive Properties**

Properties which depend upon the amount of the substance present in the system are called

**extensive properties**.

*Mass, Volume, Number of moles, Enthalpy, Entropy, Free energy, Heat Capacity, Force, Surface Area*etc are the example of extensive properties. These properties are additive. If mass of the gas is changed, the volume is also changed and so is the number of moles and their internal energy of the system.

Properties which don't depend upon the amount of the substance present in the system are called

**intensive properties**.

*Temperature, Pressure, Boiling Point, Melting Point, Specific Heat, pH, Vapour Pressure, Surface Tension, Viscosity*etc are the example of intensive properties. If temperature of a glass of water is 25

^{o}C, then each and every drop of water in this glass has the temperatue of 25

^{o}C. These properties are non additive.

**Internal Energy (E or U)**

All forms of energy associated with a system is called

**internal energy**or simply energy of the system (E).

This is expressed in Joule. This arises due to movement of molecules, arrangement of atoms in molecules, number of arrangement of electrons in atoms etc.

It is neither possible nor necessary to calculate the absolute value of internal energy of a system. It is a state function so depend only on the initial and final state of the system.

ΔE = E

_{f}– E

_{i}

In a reaction- R → P

ΔE = E

_{P}– E

_{R}

If E

_{f}> E

_{i}, ΔE is + ve

if E

_{f}< E

_{i}, ΔE is – ve

**Sign Conventions for Work and Heat**

W is +ve when work is done on the system W is – ve when work is done by the system q is +ve when the heat is being absorbed by the system q is – ve when the heat is evolved by system

**Heat Capacity**

The amount of heat required to change its temperature by one degree of a substance.

Q = CΔT

or, C = Q/ΔT

**Molar Heat Capacity**

The amount of heat required to change its temperature by one degree of one mole of a substance.

**Heat Capacity at Constant Pressure (C**

_{p})The amount of heat required to change its temperature by one degree of a substance at constant pressure.

**Heat Capacity at Constant Volume (C**

_{v})The amount of heat required to change its temperature by one degree of a substance at constant volume.

**Relation between C**

_{P}and C_{V}We know that

H = E + PV

or, H = E + RT (as PV = RT for one mole)

differentiating the above equation w.r.t T, we get-

dH/dT = dE/dT + R(dT/dT)

or, C

_{P}= C

_{V}+ R

or, C

_{P}− C

_{V}= R

**First law of Thermodynamics**

It is also called energy conservation principle. According to this principle, energy can neither be created nor be destroyed, it can only be transfer or change fron one form to another form.

In other way-

Heat absorbed (Q) by the system is equal to change in internal energy (ΔE) plus work done by the system (−W).

Q = ΔE + (−W)

or, ΔE = Q + W

*During an isothermal process,*the temperature of the system remains constant and hence ΔE = 0

so, 1st law of thermodynamics becomes-

Q = −W

or, −Q = W

Therefore, in isothermal process-

Heat absorbed by the system is equal to work done by the system or Heat evolved by the system is equal to work done on the system.

*During adiabatic process,*the system acts an isolated system and hence q = 0 so, 1st law of thermodynamics becomes-

ΔE = W

Therefore, Work done on the system is equal to increase in internal energy of the system i.e., when a gas is compressed adiabatically its internal energy increases or Work done by the system is equal to decrease in internal energy of the system, i.e., when a gas is expanded adiabatically its internal energy decreases.

*During Cyclic Process,*ΔE = 0

Q = −W

Therefore, in cyclic process, work done by the system is equal to heat absorbed by the system or work done on the system is equal to heat evolved by the system.

**Limitations**

First law does not indicate whether heat can flow from a cold body to a hot body or not.

First law does not specify that process is feasible or not.

Practically it is not possible to convert the heat energy into an equivalent amount of work.

**Work done in Isothermal and Reversible Expansion**

Let us consider 'n' moles of an ideal gas enclosed in a cylinder fitted with a frictionless, weightless and movable piston. Let P be the pressure of the gas and P-dP be the external pressure under which volume of the gas increased by dV, then work done in this expansion is

dw = −(P − dP)dV = − PdV (as dP.dV is very small).

For a infinite volume change from V

_{1}to V

_{2}, the total work done during expansion-

where P

_{1}and P

_{2}are the initial and final pressure respectively.

**Question: 3 moles mole of and ideal gas are expanded isothermally and reversibly from volume of 10 m**

^{3}to the volume 20 m^{3}at 300 K. Claculate the work done by the system. (Answer: 5.178 KJ)**Entropy (S)**

It is a thermodynamic state function that is a measure of the randomness and disorderness of the molecules of the system. Greater the randomness, greater would be entropy. It is denoted by 'S'. As it is a state function so depends upon initial and final satate only. So change in entropy

ΔS = S

_{final}− S

_{initial}

For a reversible process at constant temperature,the change in entropy is equal to energy absorbed or evolved divided by the temperature.

ΔS = q/T

If heat is absorbed, ΔS is positive and entropy increases while If heat is evolved, ΔS is negative and entropy decreases.

If heat change takes place at different temperatures, then-

dS = dq

_{1}/T

_{1}+ dq

_{2}/T

_{2}+ dq

_{3}/T

_{3}+ ... = Σ(dq

_{rev}/dT)

or, ∫ds = ∫dq

_{rev}/T

ΔS = ΔS

at equilibrium, ΔS = 0

→→→→→→→

→→→→→→→

→→→→→→→

→→→→→→→

well orderd

Low Entropy

→→→→→→→

→→→→→→→

→→→→→→→

well orderd

Low Entropy

→↑←↓→←↓→

→←↓→↑←↓→

→↓←↓→↑←↓

←↑→↓←↓→↑

Random

High Entropy

→←↓→↑←↓→

→↓←↓→↑←↓

←↑→↓←↓→↑

Random

High Entropy

**Unit**

Cal K

^{-1}

or, J K

^{-1}

**Gibbs free energy(G or F)**

Gibbs free energy is the property of the system whose decrease is the measure of the maximum external work available during the transformation of system reversibly at constant pressure and temperature and it is a state function. So depend only on initial and final state of the system.

If S is the entropy of a system at T

^{o}K and H is its enthalpy then, Gibbs free energy is mathematically expressed as-

G = H - TS

On differentiation we get,

ΔG = ΔH − TΔS − SΔT

we know that- ΔH = ΔE + PΔV + VΔP

so, ΔG = ΔE + PΔV + VΔP − TΔS − SΔT

or, ΔG = ΔA + PΔV + VΔP − SΔT (as ΔE − TΔS = ΔA (work function))

at constant pressure and temperature-

or, ΔG = ΔA + PΔV

or, ΔG = −W

_{max}+ PΔV (as W = −ΔA from 1st law of thermodynamics)

or, −ΔG = W

_{max}− PΔV

PΔV is the work done due to expansion against a constant pressure. So, decrease in free energy accompanying a process which occurs at constant pressure and temperature is the maximum work obtained from the system other than PΔV. Hence it is also called Net Work.

So, Net Work = −ΔG

**Variation of Free Energy with Temperature and Pressure**

We know that-

F = H − TS -----(equation-1)

or, F = E + PV − TS (as H = E + PV)

differentiating this equation we get-

dF = dE + PdV + VdP − TdS − SdT

or, dF = dq + VdP − TdS − SdT (as dq = dE + PdV)

or, dF = TdS + VdP − TdS − SdT (as dq

_{rev}/T = dS)

or, dF = VdP − SdT -----(equation-2)

*at constant Temperature*-

or, dF = VdP

or, (dF/dP)

_{T}= V -----(equation-3)

and

*at constant Pressure*-

or, dF = − SdT

or, (dF/dT)

_{P}= − S -----(equation-4)

**Free Energy Change of Expansion of an Ideal Gas**

When a system undergo a reversible change, the change in free energy with temperature and pressure is given as-

dF = VdP − SdT

at constant temperature-

dF = VdP

or, dF = nRT.(dP/p) (as PV = nRT)

on integrating the above equation we get-

∫dF = nRT∫dP/P

or, ΔF = nRT lnP

_{2}/P

_{1}

or, ΔF = nRT lnV

_{1}/V

_{2}(as P

_{1}V

_{1}= P

_{2}V

_{2})

**Enthalpy (H)**

It is heat contained in the system measured at constant pressure. The sum of internal energy and pressure volume (PV) energy is known as enthalpy.

H = E + PV

(-----equation-1)

It is an extensive property and also a state function so depends only on initial and final state of the system.

So, change in enthalpy

ΔH = H

_{final}− H

_{initial}

From equation-1-

ΔH = ΔE + Δ(PV) (-----equation-2)

or, ΔH = ΔE + PΔV + VΔP

at constant P-

ΔH = ΔE + PΔV (-----equation-3)

and at constant V-

ΔH = ΔE + VΔP (-----equation-4)

For chemical reactions, at constant temprature and pressure equation-2 becomes-

ΔH = ΔE + Δn

_{gas}RT (-----equation-5)

at constant P-

ΔH = q

_{p}

and at constant V-

ΔH = q

_{v}

so, equaton-5 becomes-

q

_{p}= q

_{v}+ Δn

_{gas}RT (-----equation-6)

For endothermic reaction change in enthalpy is positive and for exothermic reaction it is negative.

ΔH = +ve for Endothermic Reaction

ΔH = −ve for Exothermic Reaction

**At 27°C the internal energy change of reaction H _{2}(g) + Cl_{2}(g) → 2HCl(g) is 2Cal. What is the enthalpy change of this reaction.**

**Hess' Law**

The enthalpy change in a chemical or physical process is the same whether the process is carried out in a single step or in multiple steps. The purpose of Hess' law is to measure the enthalpies of neutralization for several acid-base reactions.

Let us consider a general chemical equation-

Reaction takes place in a single step-

A + B → D ΔH = Q

Reaction takes place in multiple steps-

A + B → C ΔH = Q

_{1}

C → D ΔH = Q

_{2}

So, according to Hess' law-

Q = Q

_{1}+ Q

_{2}

**Applications**

Followings are some important applications of Hess' law

Use to calculate heats of many reactions which do not take place directly.

Use to determine the bond enthalpies.

Use to calculate enthalpies of reactants and products.

It is useful to find out heat from extremely slow reactions.

It is useful to find out the Heat of reaction, Heat of transition, Lattice energy of the crystal, Heat of formation of intermediate compounds which are unstable.