Transcription of The thermodynamic definition of entropy
1 Nils Walter: Chem 260q > 0 Adding heat increases the entropy (and disorder) of the systemq > 0 The entropy (and disorder) of the systemincreases in an isothermal expansionThe thermodynamic definition of entropyAtkins, Chapter 4 TqSrevSys= heat that would be transferred in areversible process (= maximum heat)Why is this a suitable definition ?temperature at which heatexchange takes placeTdqdSrevSys=small changeNils Walter: Chem 260 Reversible expansionReversible expansionIrreversible expansionIrreversible expansionEntropy change in a system can becalculated from the reversible heatp2 = 1 atmV2 = 15 LT = 298 Kn = 1 molp1 = 15 atmV1 = 1 LT = 298 Kn = 1 molp2 VolumePressurep1 = 15 atm, V1 = 1 Lp2 = 1 atm, V2 = 15 Lw = kJw = = =VVnRTwrevqrev = -wrev = + kJThe system entropy increases bythe same amount in bothexpansions (state function!)The system entropy increases bythe same amount in bothexpansions (state function!)
2 === KJKTqSrev Nils Walter: Chem 260isothermal U= q + w = Cv T = 0 Classical thermodynamic definition of S in the isothermal expansion of a perfect gas:classical entropy change in theisothermal expansion of a perfect gasV1W1 (V1 )NV2W2 (V2 )NN molecules of gasHow do classical and statisticalthermodynamic definitions of SSys match?revrevqVVnRTw = =12ln;1212112 TqdqTTdqSSSrevstatestaterevstatestaterev === = = 12lnVVnRS Statistical thermodynamic definition of S in the isothermal expansion of a perfect gas: = = = 121212lnlnlnVVknNVVNkVVkSAN = 12lnVVnRS S = k ln W2 - k ln W1 = k ln (V2)N - k ln (V1)NRclassical and statistical entropy change inthe isothermal expansion of a perfect gasNils Walter: Chem 260 SUniverse = SSystem + SSurroundings 0 SUniverse = SSystem + SSurroundings 0 The net entropy will increase or staythe same.
3 It will never net entropy will increase or staythe same. It will never decrease. SSYS < 0q SSurr > 0 SSurr qT SUniv = 0 only for a reversible process SUniv > 0 for all other processesAtkins: The entropy of the universe tends to increaseAtkins: The entropy of the universe tends to increaseThe second law of thermodynamicsNils Walter: Chem = = = =VVnRTwrev SSys is a state function, while SSurr and SUniv are pathway dependentReversible expansionReversible expansionIrreversible expansionIrreversible expansionw = - p2 V = kJp2 = 1 atmV2 = 15 LT = 298 Kn = 1 molp1 = 15 atmV1 = 1 LT = 298 Kn = 1 molp2 VolumePressurep1 = 15 atm, V1 = 1 Lp2 = 1 atm, V2 = 15 Lw = kJw = kJqSys = -w = kJ SSys = J K-1 SSys = J K-1 SSurr = J K-1 SSurr = J K-1 SUniv = 0 J K-1 SUniv = 0 J K-1 SSys = J K-1 SSys = J K-1 SSurr = J K-1 SSurr = J K-1 SUniv = 9 J K-1 SUniv = 9 J K-1 TqSrevSys= TqSSysSurr = Nils Walter.
4 Chem = =+= =VVnRTwrevIsothermal compressionReversible compressionReversible compressionIrreversible compressionIrreversible compressionw = - p1 V = + kJp2 = 1 atmV2 = 15 LT = 298 Kn = 1 molp1 = 15 atmV1 = 1 LT = 298 Kn = 1 molp1 VolumePressurep1 = 15 atm, V1 = 1 Lp2 = 1 atm,V2 = 15 LqSys = -w = - kJ SSys = - J K-1 SSys = - J K-1 SSurr = + J K-1 SSurr = + J K-1 SUniv = 0 J K-1 SUniv = 0 J K-1 SSys = - J K-1 SSys = - J K-1 SSurr = + J K-1 SSurr = + J K-1 SUniv = K-1 SUniv = K-1 TqSrevSys= TqSSysSurr =
