Heat and Mass Transfer

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FUNDAMENTAL CONCEPTS
Heat transfer is energy in transit, which occurs as a result of temperature gradient or difference. This temperature difference is thought of as a driving force that causes heat to flow. The concepts of heat transfer and temperature, the key words in the discipline of heat transfer, are 2 of the most basic concepts of thermodynamics.

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System: a region in space containing a quantity of matter which is separated from its surroundings by a boundary. Closed system (no – flow system): no exchange of matter with the surroundings, only heat and work cross the boundary. Open system (flow system): there is matter exchange with the surroundings in addition to heat and work. Work (W): is a transient quantity (energy) which only appears at the boundary when a system changes its state due to the movement of a part of the boundary under the action of a force. Sign convention:

system

+

-

the work is done by the system on the surroundings: the work exits the

the work is done on the system by the surroundings.

(Although there cannot be said to be any work in a system either before or after the change has taken place, work may be said to “flow” or be “transferred” across the boundary.) Heat (Q): is “something” (energy transfer), which only appears at the boundary when a system changes its state due to a difference in temperature between the system and its surrounding. Heat, like work, is a transient quantity, which only appears at a boundary while a change is taking place within the system. (Although there cannot be said to be any heat in a system before and after a change of state, loosely speaking heat may be said to “flow” or be “transferred” across the boundary. Strictly speaking it is energy which is transferred, but to say “heat is transferred” is a shorthand way of saying “the energy transferred by virtue of a temperature difference.”) Sigh convention: +

-

if heat flows into a system from the surroundings:
If heat flows from the system to the surroundings.

1.1 First Law of Thermodynamics
It is the principle of conservation of energy. It is an axiom. The first law of thermodynamics says that there exists a property of a closed system (U) such that a change in its value is equal to the difference between the heat supplied and the work done during any change of state: 1

2

b

c

X δ Q @ δ W = U 2 @U 1
1

where U is the internal energy, J

Writing Q and W for the quantities of heat and work crossing the boundary during the change of non heat energy equation
state: Q-W=U2-U1
By words: any quantity of heat supplied to a closed system must equal the increase of internal energy plus the work done by the system.
The internal energy of a closed system remains unchanged. For isolated systems Q=0, W=0 therefore ∆U = 0
For irreversible non-flow processes the energy equation can only be applied in integrated form:

Q @ W = ∆U
For reversible processes, the energy equation can only be applied in differential form: V

W

d Q @ δW = d U
δ Q @ pdV = dU
δ W = pdV

For reversible, constant pressure processes (closed system): b

c

b

c

p = constant [ pdV = d pV [ δ q @ d pV = dU
b

c

δ Q = d U + pV = dH where H = enthalpy, J
or Q = ∆H

Steady-flow energy equation (for open system)
b
c1b
c
`
a
f
f
2
Q @ W = H 2 @ H1 + fm v 2 @ v12 + mg z 2 @ z1
2

The potential energy term is either zero or negligible compared with the other terms. The 1st law of thermodynamics does not make any distinction between heat transfer and work transfer: to it they are both energy “interactions” (non-properties) that must be distinguished from the energy change (property)

1.2 Second Law of Thermodynamics
It is an axiom. It says that it is impossible to construct a system which will operate in a cycle, extract heat from a...
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