The document Polytropic Process, Entropy Change and Spontaneity Class 11 Notes | EduRev is a part of the Class 11 Course Chemistry for JEE.

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**POLYTROPIC PROCESS**

PV^{x} = Const

**MOLAR HEAT CAPACITY OF POLYTROPIC PROCESS**

dU = dq + dW

nC_{V}dT = nC_{m}dT (-PdV)

PV = nRT

KV^{-x }V = nRT

kV^{-x 1} = nRT

**Limitations of First law of Thermodynamics****(a)** First law of thermodynamics does not give information regarding the direction of propagation of a process**(b) **First law of thermodynamics does not tell us why an equilibrium is attained.**(c) **First law of thermodynamics does not tell us when an equilibrium will be attained.**(d) **First law of thermodynamics does not give information about why there can not be 100 percent conversion of heat into work

**Second Law of Thermodynamics****Statement(I) : **Second law of thermodynamics states that heat can never be converted into work with 100% efficiency**Statement(II) : **No engine in this world can be constructed which operates in cycles and converts all the heat from source to work.**Statement(III) : **No refrigertator can be designed which operates in cycles and rejects heat from sink to source, perpetually (self - functioning).**Entropy : **Entropy is the direct measurment of randomness or disorderness. Entropy is an extensive property & it is a state function

for reversible process. entropy is related with complexity of the molecule within the system.

EtOH > MeOH

C_{2}H_{6} (g) > C_{2}H_{5}(g)

N_{2}O_{4} > NO_{2}

O_{2} > N_{2} (molecular wt.)

Gas > Liq > Amorphous solid > crystalline solid

**Entropy always increases in the following process ****(a)** s → ℓ, ℓ → g, s → g,**(b) **Isothermal expansion of ideal gas.**(c)** Mixing of two non reacting gases.**(d)** In chemical reaction in which

Δn_{g} > 0**(e)** Heating of any substance

**Classification of process Based on spontaneity**

**Why Spontaneity**

**Points to ponder: **

Why a system always moves towards disorderness ?**Answer: **A system moves towards disorderness because the probability of moving towards disorderness is very high.**DISORDERNESS**

**For Reversible process: **

**Note : Irreversible process**

The entropy change for an irreversible process can be calculated by substituting it with equivalent reversible process. Both will have same entropy change.

**Entropy Change of Universe**

ΔS_{universe} = ΔS_{system} ΔS_{surrounding}

**Spontaneity**

**1. **Δ**S _{universe} > 0 ⇒ Spontaneous **

**2. **Δ**S _{universe} = 0 ⇒ Equilibrium **

**3. **Δ**S _{universe} < 0 ⇒ Non-spontaneous. **

**Entropy Change**

**Calculation of entropy change**

**(A) General heating or cooling**

If C is temperature independent

If C is a function of Temperature

C = a + bT

**(B) In phase transformation **

*A_{(l)} A_{(g)}.

*A_{(s)} A_{(g) }

**(C) Entropy change during chemical reaction. **

aA bB → cC dD

ΔSº = entropy of product - entropy of reac tan t

For any chemical reaction

**(D) Calculation of entropy change during expansion/compression of ideal gas from P _{1}V_{1}T_{1} to P_{2}V_{2}T_{2}**

From I^{st} law of thermodynamics

dE = dq + dW

dq = - dW + dE

TdS = PdV + nC_{V}dT

For ideal gas

ΔS = nC_{V}ln + nRln .

= nC_{V}ln nRln nRln

**Calculation of entropy change during isothermal Expansion; **

because

W_{rev} > W_{irr }

ΔS_{total} = +ve

**Calculation of entropy change during isothermal compression. **

q_{irr} + w_{irr} = 0

| w_{irr} | > | w_{rev} |

< 0 >0

⇒ | q_{irr }| > | q_{rev }|

**Calculation of entropy change during for adiabatic expansion of ideal gas.**

**For reversible process **

Where K is constant

**For irreversible process **

**This means that the final temperature of irreversible process is greater than reversible process.**

ΔS = nC_{V} ln + nRln

-ve +ve

= nC_{V}ln - nC_{V}ln

⇒ T'_{2} > T_{2}

⇒ ΔS = +ve

⇒ ΔS_{total} = +ve

**Calculation of entropy change in adiabatic compression. **

dT = 110

For reversible

(T_{2} - T_{1}) = 100K

T_{2} = T_{1} + 100 K

for irreversible

T^{'}_{2}= T_{1} 110 K

T^{'}_{2 }> T_{2}

_{}

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