섹션 개요

    • Introduction of thermodynamic functions

      Here, the thermodynamic equation finally comes into play in order to better understand entropy.

       

      【First law of thermodynamics】

      　When heat (⊿Q) is added to an object, it is used to increase the internal energy of the object (⊿U) and change the volume of the object (work = P⊿V).

      　P is pressure and ⊿V is volume change. 

                                  ⊿Q ＝ ⊿U ＋ P⊿V

       

      【Ideal gas law】

      　Volume (V) is inversely proportional to pressure (P) and proportional to temperature (T)

       

                                  PV = nRT　　→　PV = RT, per mol.

       

      　　　　　　　　R：gas constant、T：absolute temperature(K)

       

      【Internal energy (U) is proportional to temperature】（For now, I hope you believe that. I'll add more later.）

       

      U = n3/2・RT　→　U = 3/2・RT, per mol.

       

      Internal energy change is, ⊿U = 3/2・R⊿T.


                                                                                                                                   

       

      Based on these, we calculate the entropy change when changing from state 0 (T0, V0) to state 1 (T1, V1).

       

      Definition of entropy change：　⊿S ＝ ⊿Q／T

       

      ⊿S = ⊿Q／T = ( ⊿U + P⊿V)／T

          = (3/2・R⊿T ＋ P⊿V)／T

          =3/2・R⊿T／T ＋ R⊿V／V                         （Transformation of the ideal gas law：1／T = R／PV）

          =3/2・R （∫1/T dT） ＋ R（∫1/V dV）　　　←At the integral, T0→T1 and V0→V1.

          =3/2・R・Ln(T1／T0) ＋ R・Ln(V1／V0)

    • Here we have the important equation to calculate the entropy change from state 0 (T0, V0) to state 1 (T1, V1).

       

      ⊿S = ⊿Q／T

          =3/2・R・Ln(T1／T0) ＋ R・Ln(V1／V0)

       

      (The above equation is the entropy change per mole. n should be multiplied by n when dealing with n moles of material.)