hukum ii termodinamika , hubungan suhu dengan volume

Kimia Fisika I - BAB III 1

4.2.1 entropy as a function of temperature and volume

If the entropy is a function of temperature and volume, mathematically expressed as follows

S = S(T,V) (4.13)


Expressed in terms of total differential equations

Equation (4.14) states the entropy change if the temperature and volume changes, each of dT and dV. Evaluation of the quotient in equation (4:13) is indispensable for menghiitung value overall entropy change, as a result of changes in the two variables.

To evaluate these two quotients can be done with the help of the First Law of Thermodynamics formulation, namely

dU=dQrev+dWrev

(4.14)dVV

SdT

T

SdS

TV


If the process is reversible and the work done is only a working volume, then

dQrev = dU + PdV (4.15)

To obtain the change in entropy, equation (4.15) divided by temperature, so that the resulting

)16.4(T

P

T

1dVdUdS


dU as fungsi T dan V is expressed by

substitution of this equation to dU into equation (4.16)

yields the equation

dan

dVV

UdTC

TV

dV T

P dV

V

U

T

1dTC

TV

dS


Based on the equation (4.14) and equation (4:17) obtained relationships both quotients are being sought, namely :

(4.18)TT

S

v

Cv


Further evaluation of these quotients are still needed, especially for Equation (4.19), in order to calculate the overall entropy change. If the process takes place at constant volume, then the equation (4.17) becomes

Equation (4.20) is used to calculate the change in entropy of the system at fixed volume.

If the process takes place at a constant temperature, then the equation (4.17) becomes


In contrast to equation (4:20), Equation (4:21) remains to be evaluated, because it still has another difficult quotients determined experimentally. To evaluate reached by taking the derivative of equation (4.18) and Equation (4:19). If equation (4.18) was revealed to the volume, then the equation is obtained as follows:


If equation (4.19) downgraded to temperature, then the following equation is obtained.

Since S is a function of the state of dS is an exact differential, so the derivative of S to T and V have the same value as the derivative S to V and T.


By using Equation (4.25), substituting Equation (4.23) into Equation (4.24) yields

By comparing Equation (4.19) and Equation (4.26) obtained the following relationship


With the help of cyclic rule, which is applied to the variables V, P, and T obtained relationship


With and respectively - each is the coefficient of thermal expansion and compressibility coefficient, whose value can be determined each of the experiments. Through substitution of Equation (4.27) and into the equation (4.28) apparently found that quotients (none other than the comparison value of the coefficient of thermal expansion coefficient of compressibility. From the description above, the total differential of entropy as a function of temperature and volume, with the substitution of equations (4.18) and Equation (4.28) into the equation (4.14) is

To determine the change in entropy of the system as a result of changes in temperature and volume

can be done by integration of Equation (4.29).

hukum ii termodinamika , hubungan suhu dengan volume

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