PVx = Const
MOLAR HEAT CAPACITY OF POLYTROPIC PROCESS
dU = dq + dW
nCVdT = nCmdT (-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
C2H6 (g) > C2H5(g)
N2O4 > NO2
O2 > N2 (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
Δng > 0
(e) Heating of any substance
Classification of process Based on 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.
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
ΔSuniverse = ΔSsystem ΔSsurrounding
1. ΔSuniverse > 0 ⇒ Spontaneous
2. ΔSuniverse = 0 ⇒ Equilibrium
3. ΔSuniverse < 0 ⇒ Non-spontaneous.
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
(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 P1V1T1 to P2V2T2
From Ist law of thermodynamics
dE = dq + dW
dq = - dW + dE
TdS = PdV + nCVdT
For ideal gas
ΔS = nCVln + nRln .
= nCVln nRln nRln
Calculation of entropy change during isothermal Expansion;
Wrev > Wirr
ΔStotal = +ve
Calculation of entropy change during isothermal compression.
qirr + wirr = 0
| wirr | > | wrev |
< 0 >0
⇒ | qirr | > | qrev |
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 = nCV ln + nRln
= nCVln - nCVln
⇒ T'2 > T2
⇒ ΔS = +ve
⇒ ΔStotal = +ve
Calculation of entropy change in adiabatic compression.
dT = 110
(T2 - T1) = 100K
T2 = T1 + 100 K
T'2= T1 110 K
T'2 > T2