- #1
Another
- 104
- 5
- Homework Statement
- adiabatic process equation derivation
- Relevant Equations
- dU = U_V dT + U_T dV ; U_V is derivative U by T (volume constant) and U_T is derivative U by V (temperature constant)
dQ = dU + p dV
in this textbook : http://www.fulviofrisone.com/attach...tatistical Mechanics 2Ed (Wiley)(T)(506S).pdf ;page 20
I don't understand about Eq 1.11 come to 1.12 ? I know
dU = U_V dT + U_T dV
dQ = dU + p dV
put dU into dQ. So dQ = U_V dT + (U_T +p) dV
and i know that c_v = U_V = dU/dT when volume constant. So
dQ = c_v dT + (U_T +p) dV
and dS = dQ/T .
dS = c_v/T dT + 1/T (U_T +p) dV and ds is exact differential
d/dV ( c_v / T) = d/dT ((1/T)(U_T +p)))
i think derivative of c_v/ T by dV when T (Temperature constant) Equal to 0 . but I not sure
I need someone to explain to me. why Eq 1.11 come to Eq 1.12