Page 24 - Advanced thermodynamics for engineers

1.5 INTERACTIONS BETWEEN SYSTEMS AND SURROUNDINGS 7

~
In other systems of units J is not unity, e.g. in imperial units (foot, pound, second) the value
~
~
of J ¼ 778 ft lb=Btu, while in the cgs (centimetre–gram–second) system the value of J is
4.1868 g cm/cal.
While Eqn (1.5) shows the proportionality of heat and work around a cycle, it does not give any
information about intermediate states around the cycle. However, it is possible to introduce the concept
of internal energy.

1.5.5 INTERNAL ENERGY
The quantity R ðdQ dWÞ is independent of the process and is dependent only on the end states. This
means that R ðdQ dWÞ is a thermodynamic property, and it is named internal energy denoted by the
symbol E. The change in internal energy, E, in a process from 1 to 2 is
Z 2
E 2 E 1 ¼ ðdQ dWÞ; (1.6)
1
or
dE ¼ dQ dW: (1.7)
Equations (1.6) and (1.7) define the First Law in integrated or differential form. They both define
the conservation of energy, which states that the change in energy of a system is equal to the algebraic
sum of the heat and work transfers to the system.
Both Eqns (1.6) and (1.7) relate the change in internal energy to the heat and work transfers. They
do not define the datum level of internal energy.

1.5.5.1 Relationship between E, Q and W
• The change in internal energy around a cycle is always zero.
• The net quantityofwork(dW) and heat (dQ) transfers around a cycle will not necessarily be zero.
• The change of internal energy, E 2 E 1 has a significance as a quantity associated with the
state of a system.
• Work, heat and internal energy are all energy terms.
• Work and heat are both transitory energy transfers at the control surface of a system.
• Internal energy is the energy of the interior of the system.

1.5.5.2 Isolated systems
If a system executes a process in which no heat or work transfers occur then the system is said to be an
isolated system. The internal energy of an isolated system is constant.

1.5.5.3 Energy of a system
The energy of a system was defined as E, without being specific about the form of this energy. Work
transfer can bring about changes to many forms of energy: kinetic energy, potential energy, magnetic,
capillary, electrical and thermal energy. In this analysis only kinetic, potential and thermal energy will
be considered because these are the main forms of energy encountered by the mechanical engineer.
The analysis can be expanded to include the other forms if necessary. Heat transfer can only, primarily,
affect the thermal energy.