Energry Balance For Closed System

 

ENERGY BALANCE FOR CLOSED SYSTEM

"If the matter does not transfer from boundary to surrounding or from surrounding to system then this type of system is known as closed system and mass of closed system should be constant, However energy can cross the boundary." One can easily develop basic concepts in thermodynamics by carefully observing system.

Most of industrial processes are open system, in which matter crosses the system boundary as streams that enter and leave process equipment.

No streams enter or leave the closed system, no energy associated with the matter is transported across the boundary that divides the system from surroundings. All energy transfer between a closed system and surroundings is in the form of heat or work. Total energy change of the surroundings equals the net energy transferred to or from it as heat and work only.

∆ (Energy of the system) + ∆ (Energy of the surroundings) = 0..........Eq (1)

Second term of equation may be replaced by variables which represents as heat and work, to get.

∆ (Energy of surroundings) = ± Q ± W..........Eq (2)

Where Q is heat and W is work to the system. And the sign for numerical value depends in which direction heat and work is flowing with respect to the system or surroundings.

If we adopt the convention that makes the numerical values of both quantities positive for transfer into the system from surroundings. The corresponding quantities taken with reference to the surroundings, Q_surr and W_surr , have the opposite sign. Q_surr = -Q and W_surr = -W.

∆ (Energy of surroundings) = Q_surr + W_surr = - Q - W..........Eq (3)

With this logic equation 1 becomes:

∆ (Energy of system) = Q + W Eq..........(4)

Equation 4 indicates that the total energy change of a closed system equals the net energy transferred into it as heat and work.

In closed system often undergo processes in which change in external energy is zero only the internal energy of the system changes. Foe this type of processes equation 4 becomes:

∆ U^t = Q +W Eq..........(5)

Where U^t is the total internal energy of the system. For differential changes in U^t :

dU^t = dQ+ dW  Eq..........(6)

In equation 3, equation 4, equation 5 and equation 6 all terms require to be expressed is same energy units. For SI system unit of the energy is joule (J). For British system unit of energy is (British Thermal Unit).

For closed system containing n numbers of moles, equation 5 and equation 6 becomes

∆ (nU) = n(∆U) = Q +W  Eq..........(7)

d(nU) = n(dU) = dQ +dW  Eq..........(8)

In this form, these equations show explicitly the amount of substance comprising the system.

These equations of thermodynamics are many times written for a certain unit amount of material, either a unit mole or unit mass. For n=1 equation 7 and equation 8 becomes:

∆ U = Q +W and dU = dQ + dW

Above equations do not provide a definition of internal energy. Indeed, they presume prior affirmation of the existence of internal energy, as expressed in the following axiom:

Axiom 1: There exists a form of energy, known as internal energy U, which is an intrinsic property of a system, functionally related to the measurable coordinates that characterize the system. For a closed system, not in motion, changes in this property are given by Eq. (7) & (8).

Equations 7 and 8 not only helps to calculate changes in internal energy from experimental measurements, but they also helps us to derive the property relations that connects directly to measurable quantities like temperature and pressure. These two equation have dual purpose, because once internal energy values are known, they provide for the calculation of heat and work quantities for practical processes. By accepting the above axiom and associated definition of a system and surroundings, one can state the first law of thermodynamics as a second axiom:

Axiom 2: (The First Law of Thermodynamics) The total energy of any system and its surroundings is conserved.