Spontaneous processes and the negative values of the changes in Gibbs energy values.
The description with regard to Gibbs energy.
We have established a simple method for description with regard to spontaneous phenomena, by means of a change in the thermodynamic function in a system.
That's a function called Gibbs energy(G) as follows.
G=H-TS
G is Gibbs energy and is measured in calories or joules.
H is enthalpy and is measured in calories or joules.
T is the absolute temperature and is measured in K⁰ (degrees K) (absolute zero is -273.15℃).
S is entropy and is measured in calories/absolute temperature or joules/absolute temperature.
Let's try to trasform the formula of the second law of thermodynamics which describes spontaneous processes.
ΔSuniv = ΔSsys ＋ΔSsurr ≧ 0 (the second law of thermodynamics)
The entropy is the value which is obtained by dividing amount of heat(Q) by the temperature(T).
S(entropy)=Q/T and so ΔSsurr=ΔQsurr/T.
When the temperature of the system is in thermal equilibrium with the surrouding environment,
the temperature of the system is constant and the amount of hest entered and exited is equal.
ΔQsurr/T= - ⊿Qsys/T and the sign is reversed.
After rewritten the equation ΔSuniv = ΔSsys ＋ ΔSsurr ≧ 0 to the equation ΔSuniv = ΔSsys-Δ Qsys／T ≧ 0,
multiply by -T to the both sides of the equation to make the equation -T⊿Suniv = ΔQsys - TΔSsys ≦ 0.
When given the equation ΔG=-TΔSuniv, the equationΔG=ΔQsys -TΔSsys≦0 is obtained, Gibbs energy(G) is described as the equation G=Qsys - TSsys.
If you apply an amount of heat to a gas under constant pressure, in addition to the increase in internal energy, the gas expands and does work(W) to the surrounding evironmment.
Because of the reason why is metioned above, when considering the entire energy of the gas, it's neccessary to consider energy that's separate from the internal energy(U).
From this point of view, the entire energy of the gas which consists of the sum total of internal energy(U) and the work(W) in the surrounding environment is enthalpy(H).
The work which is done to the surrounding environment is described by the following formula.
W=PV
where
P is pressure and the unit is atmospheric pressure (atm).
V is the volume and the unit is liters (l).
1 l atm (one liter atmospher) = 0.10204kj ≈ 0.1kj (zero comma one kilojoules).
H = U + PV
G = Qsys - TSsys
where
Qsys is the amount of heat applied to a system that may contain gases.
Due to Qsys = Hsys, G =Qsys - TSsys = Hsys - TSsys.
Since the formula results n the thermodynamic function in a system, the letter sys is omitted.
The following formula is established.
G=H-TS
Under constsnt temperature (Conditions under which temperarure changes can be ignored ),
the amount of the changes in Gibbs energy value(G) is described as follows.
ΔG=ΔH-TΔS
When ΔG=ΔH-TΔS≦0, the change of the system is spontaneous.
The formulas ΔG=ΔQsys -TΔSsys≦0 and ΔG=ΔH-TΔS≦0 are the same description.
By evaluating the amount of change in Gibbs energy of the system, it is possible to judge the spontaneous process.
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Reference:
Physical Chemistry for the Bioscience Written by Raymond Chang Translated by Iwasawa Yasuhiro, Kitagawa Teizou, Hamaguchi Hiroo TOKYOKAGAKUDOJIN Co., Ltd.
ENTROPY AND THE SECOND LAW Written by ARIEH BEN-NAIM Translated by Ono Yoshiyuki Maruzen-publishing Co.,Lid.
https://www.jstage.jst.go.jp/article/biophys/41/2/41_2_74/_pdf/-char/ja
