 # Spontaneity and Change in Entropy

Change in entropy (ΔS) :
\triangle S = \frac{q_{rev}}{T}
qrev = heat given to the system reversibly and isothermally.
Calculation of ΔS of phase transition :
melting of Ice (fusion)
ΔHfusion = 6 kJ / mol = qrev
\triangle S = \frac{6000}{273}
\triangle S = \frac{\triangle H _{vap}}{B.pt}
ΔStotal = ΔSsystem + ΔSsurrounding > 0

Spontaneous Property :
ΔG = −ve : spontaneous
ΔG = +ve : Non spontaneous
ΔG = 0 : equilibrium

Criteria of Spontaneity :

 ΔH ΔS ΔG condition −ve +ve −ve (Sp) ΔH > TΔS −ve −ve −ve (Sp) (at low T) +ve +ve −ve (Sp) |T.ΔS| > |ΔH| +ve −ve +ve at high T non spontaneous + + + (non spontaneous) at low T

### Part2: View the Topic in this Video from 1:08 to 31:40

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1. \tt \triangle S = nC_V \ ln \left(\frac{T_{2}}{T_{1}}\right)+nR \ ln \left(\frac{V_{2}}{V_{1}}\right)

2. \tt \triangle S_{melting} =\frac{\triangle H _{fusion}}{T_{m}}

Tm = melting point of substance

3. \tt \triangle S_{vaporisation} =\frac{\triangle H _{vaporisation}}{T_{b}}

Tb = boiling point of substance

4. \tt \triangle S_{sublimation} =\frac{\triangle H _{sublimation}}{T_{sub}}

Tsub = sublimation temperature