THERMODYNAMICS  THEORY



Energy Balance for Closed Systems

Energy Balance for Closed System 

The energy balance for a system, which has been previously
introduced, is:
(Q_{in}  Q_{out} ) + (W_{in}  W_{out})
+
(E_{mass,in}  E_{mass,out})
= ΔE_{system} = (ΔU
+ ΔKE + ΔPE)_{system}
_{ }For
a closed system, the only forms of energy that can be supplied or removed
from a system are heat and work.
(Q_{in}  Q_{out} ) + (W_{in}  W_{out}) = (ΔU
+ ΔKE + ΔPE)_{system
}




Sign Convention for Heat Transfer
Sign Convention for Work


If the adopted sign convention is such that the heat
entering the system is positive, and the work done by the system is positive
for a process from state 1 to state 2, then the energy balance for a closed system becomes:
Q  W = E_{2}  E_{1 }= ΔE_{system}
= (ΔU
+ ΔKE + ΔPE)_{system}
For a stationary system, in which no velocity and elevation changes
during a process, the change of the total energy of the system is due
to the change of the internal energy only. That is,
Q W = U_{2}  U_{1
} 



Specific Heats of Solids and Liquids



The definitions of constant
volume and constant pressure specific heats have been introduced previously. They are
For most solids and liquids, they can be approximated as incompressible
substances, hence the constant volume and constant pressure specific
heats are the same. That is,
c_{P} = c_{v} = c
The specific heats of incompressible substances depend on the temperature
only. Hence the specific heats are simplified as:
c_{v} = du/dT c_{P} =
dh/dT






Internal Energy and Enthalpy Difference of Solids
and Liquids



From the definition of specific heat, the change of internal energy
becomes
du = c_{v}dT
= c(T) dT
For a process from state 1 to state 2, the change of internal energy
is obtained by integrating the above equation from state 1 to state 2.




Internal Energy and Enthalpy of
Solids and Liquids 

For small temperature intervals, an average specific heat (c)
at the average temperature is used and treated as a constant, yielding
Enthalpy is another temperature dependent variable. The definition of enthalpy is:
H = U + PV
It can be rewritten in terms of per unit mass as follows:
h = u+ Pv
Note that v is a constant, so the differential form of the above equation is:
Integrating from state 1 to state 2 yields
Δh = Δu + v ΔP + vΔP
For solids, the term vΔP is insignificant.
Δh = Δu
For liquids, two cases are encountered. They are:
 Constant pressure process, ΔP = 0, Δh = Δu
 Constant temperature process, ΔT = 0, Δh = vΔP



