Entropy

Entropy

Entropy is a measure of randomness or disorder of the system.

The greater the randomness, higher is the entropy.

Solid state has the lowest entropy, the gaseous state has the highest entropy and the liquid state has the entropy in between the two.

Entropy is a state function. The change in its value during a process, is called the entropy change.

ΔS = S₂ -S₁ = ∑S _products – ∑S _reactants 

1) When a system absorbs heat ,the molecules start moving faster because kinetic energy increases. Hence, disorder increases. More the heat absorbed ,greater is the disorder.

2) For the same amount of heat absorbed at low temperature, the disorder is more than at high temperature. This shows that entropy change is inversely proportional to temperature.

ΔS = q_rev / T

Entropy change during a process is defined as the amount of heat ( q ) absorbed isothermally and reversibly divided by the absolute Temperature ( T ) at which the heat is absorbed.

The units of entropy change are cal/K/mol in CGS system and joules/K/mol in S.I. system

The physical significance of entropy is that many processes which are accompanied by an increase of entropy are also accompanied by an increase of randomness or disorder.

 

Entropy as a state function

Consider a system consisting of a cylinder containing a gas at fitted with frictionless and weightless piston and placed in contact with the large heat reservoir.

The system absorbs heat q isothermally and reversibly at temperature T and expands from volume V₁ to V₂.

ΔS = q_rev / T

As equivalent amount heat is lost by the reservoir,

Change in entropy of the reservoir,

ΔS = − q_rev / T

Total change in entropy ΔS₁ =  ΔS_sys  +   ΔS_res  = q_rev / T + ( − q_rev / T ) =0

If we compress the gas isothermally from volume V₂ to V₁, heat q_rev will be given out by the system and absorbed by the reservoir so that ΔS = − q_rev / T and ΔS = q_rev / T

Total change in entropy ΔS  =0

Entropy changes during phase transformation

Entropy of fusion

When a solid melts, there is an equilibrium between the solid and the liquid at the melting point. The heat absorbed is equal to the latent heat of fusion.

Entropy of fusion is the change in entropy when 1 mole of a solid substance changes into liquid form at the melting temperature.

Δ_fus S = S_liq − S_solid = Δ_fus H / T_m

where

Δ_fus S is the entropy of fusion

S_liq is the molar entropy of the liquid

S_solid is the molar enthalpy of the solid

Δ_fus H is the enthalpy of fusion per mole

T_m is the melting temperature in degree Kelvin

 

Enthalpy of vaporisation

When a liquid evaporates at the boiling point ,there is an equilibrium between the liquid and the vapour.

The heat absorbed is equal to the latent heat of vaporisation.

Entropy of vaporisation is the entropy change when 1 mole of a liquid changes into vapour at its boiling point.

Δ_vap S = S_vap − S_liq = Δ_vap H / T_b

where

Δ_vap S is the entropy of vaporisation

S_liq is the molar entropy of the liquid

S_vap is the molar enthalpy of the vapour

Δ_vap H is the enthalpy of vaporisation per mole

T_b is the boiling temperature in degree Kelvin

Entropy of sublimation

Sublimation involved an equilibrium between the solid and the vapour.

Entropy of sublimation is the entropy change when 1 mole of the solid changes into vapour at a particular temperature.

Δ_sub S = S_vap − S_solid = Δ_sub H / T

where

Δ_sub S is the entropy of sublimation

S_vap is the molar entropy of the vapour

S_solid is the molar enthalpy of the solid

Δ_fus H is the enthalpy of sublimation

T is the temperature in degree Kelvin

Entropy increases when the number of molecules of the product is greater than the number of molecules of the reactants.

Spontaneity in terms of entropy change

Consider the following processes:

1)Mixing of the two gases on opening the stopcock

2)Spreading of a drop of ink in a beaker filled with water

These processes do not involve any exchange of matter and energy with the surrounding.Hence they are isolated systems.

These processes are accompanied by increase of randomness and hence increase of entropy i.e. fro these processes, entropy change is positive.

Consider the following processes:

1) Cooling down of a cup of tea

2)Reaction taking place between a piece of marble or sodium hydroxide and Hydrochloric acid in an open vessel.

These processes involve exchange of matter and energy with the surrounding.Hence they are not isolated systems.

 

For these processes, we have to consider the total entropy change of the system and the surrounding.

ΔS_total = ΔS_system +  ΔS_surrounding

For the process to be spontaneous, ΔS_total must be positive.

For all spontaneous processes, the total entropy change ( ΔS_total ) must be positive.

ΔS_total = ΔS_system +  ΔS_{surrounding .} >0

The randomness and hence the entropy keeps on increasing till ultimately an equilibrium is reached.

The entropy of the system at equilibrium is maximum and there is no further change in entropy i.e. ΔS =0.

If S_total  is negative, the direct process is non-spontaneous whereas the reverse process may be spontaneous.

1)If ΔS_total or ΔS_universe is positive, the process is spontaneous.

2)If ΔS_total or ΔS_universe  is negative, the direct process is non-spontaneous whereas the reverse process may be spontaneous

3)If ΔS_total or ΔS_universe  is zero, the process is in equilibrium.

Second Law Of Thermodynamics

All spontaneous processes are thermodynamically irreversible.

or

Without the help of an external agency, a spontaneous process cannot be reversed.

For Ex: Heat cannot by itself flow from a colder to hotter body.

or

The complete conversion of heat into work is impossible without leaving some effect elsewhere

or

All spontaneous processes are accompanied by a net increase of entropy i.e. for all the spontaneous processes, the total entropy change of the system is positive.