Chapter 4:
Work and Heat
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Part I - Work
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WORK
• is usually defined as a force F acting
through a displacement x, the displacement
being in the direction of the force.
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Power
• is rate of doing work
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Specific Work
• is the work per unit mass of the control
volume contents
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WORK DONE AT THE MOVING BOUNDARY
OF A SIMPLE COMPRESSIBLE SYSTEM
DURING A QUASI-EQUILIBRIUM PROCESS:
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Note:
Sign Convention for work:
•Work done by the system is
positive ( outflow of energy)
•Work done on the system is
negative ( inflow of energy )
• No work is done if the volume does not change.
• Work depends on P as a function of V.
• Work depends on the specific path between states 1 and state 2. Hence,
work is called a path function. We can’t integrate δW without knowing
the relationship between P and V.
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WORK WHICH DO NOT INVOLVE
MOVING BOUNDARY
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The minus sign indicates that a positive displacement results from work being supplied to
the system. If we limit the problem to within the elastic limit, where E is the modulus of
elasticity, σ is the stress, ε is the strain, and A is the cross-sectional area, then,
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Sample Problem 1
• A force F, is proportional to x2 and has a
value of 133 N when x = 2. Determine the
work done as it moves an object from x = 1
to x = 4 , where x is in meters.
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Sample Problem 2
• Air at 200 kPa, 30°C is contained in a
cylinder/piston arrangement with initial
volume 0.1 m3. The inside pressure balances
ambient pressure of 100 kPa plus an
externally imposed force that is proportional
to V0.5. Now heat is transferred to the system
to a final pressure of 225 kPa. Find the final
temperature and the work done in the
process.
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Answers
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Part II Heat
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HEAT
• defined as the energy crossing a system's
boundary because of a temperature
difference between the system and the
surroundings
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•
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Heat transferred to a system is considered positive, and;
heat transferred from a system is negative.
Thus, positive represents energy transferred to a system, and
negative heat represents energy transferred from a system.
The symbol Q represents heat.
A process in which there is no heat transfer ( Q = 0 ) is called an
adiabatic process.
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• The rate at which heat is transferred to a
system is designated by symbol
• It is also convenient to speak of the heat
transfer per unit mass of the system, q, often
termed “specific heat transfer,” which
defines as
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MODES OF HEAT TRANSFER
• Heat transfer is the transport of energy due
to a temperature difference between
different amounts of matter.
• Classification of Heat Transfer:
– Conduction
– Convection
– Radiation
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Conduction
• is the transfer of heat through molecular
interactions. For liquids and gases, the kinetic
energy of the molecules is transferred by random
molecular motion and collision. For solids, the
energy is transferred by movement of electrons or
vibration of the solid lattice.
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Fourier’s Law
For heat conductance across a plane, at steady state, with k
constant:
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CONVECTION
•
is the transfer of heat through a combination of molecular
interaction and bulk movement of gas or liquid.
• In theory, the energy balance can be set up for a
differential control volume, the energy balance equation
developed, then solved, based on fundamental physical
properties. However, this is typically too complex to solve.
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Newton’s law of cooling:
NOTE:
h depends upon the physical properties of the fluid and also upon surface
geometry, fluid velocity, and temperature. It is typically estimated using
empirical correlations.
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RADIATION
• is the transfer of heat through electromagnetic
radiation. Radiation can occur in a vacuum.
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Sample Problem 1
• The sun shines on a 150 m2 road surface so
it is at 450C. Below the 5-cm-thick asphalt,
average conductivity of 0.06 W/m⋅K, is a
layer of compacted rubble at a temperature
of 150C. Find the rate of heat transfer to the
rubble.
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Solution # 1
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Sample Problem 2
• The black grill on the back of a refrigerator
has a surface temperature of 350C with a
total surface area of 1m2. Heat transfer to
the room air at 200C takes place with an
average convective heat transfer coefficient
of 15 W/m2-K. How much energy can be
removed during 15 minutes of operation?
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Solution # 2
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Sample Problem 3
• A radiant heat lamp is a rod, 0.50 m long
and 0.50 cm in diameter, through which 400
W of electric energy is deposited. Assume
the surface has an emissivity of 0.90 and
neglecting incoming radiation. What will
the rod surface temperature be?
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Solution # 3
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COMPARISON OF HEAT AND
WORK
At this point it is evident that there are many
similarities between heat and work.
1.Heat and work are both transient phenomena. Systems never
possess heat or work, but either or both cross the system
boundary when a system undergoes a change of state.
2.Both heat and work are boundary phenomena. Both are
observed only at the boundary of the system, and both
represent energy crossing the boundary of the system.
3.Both heat and work are path functions and inexact
differentials.
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Quiz on
Heat and Work
this
December 10, 2012 (Monday),
9:00PM
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