534
CHAPTE R 18 TE M PE RATU R E, H EAT, AN D TH E FI RST L AW OF TH E R M ODYNAM ICS
Heat Transfer Mechanisms
We have discussed the transfer of energy as heat between a system and its environment, but we have not yet described how that transfer takes place. There are
three transfer mechanisms: conduction, convection, and radiation. Let’s next examine these mechanisms in turn.
Conduction
If you leave the end of a metal poker in a fire for enough time, its handle will get
hot. Energy is transferred from the fire to the handle by (thermal) conduction
along the length of the poker. The vibration amplitudes of the atoms and electrons of the metal at the fire end of the poker become relatively large because
of the high temperature of their environment. These increased vibrational amplitudes, and thus the associated energy, are passed along the poker, from atom to
atom, during collisions between adjacent atoms. In this way, a region of rising
temperature extends itself along the poker to the handle.
Consider a slab of face area A and thickness L, whose faces are maintained
at temperatures T H and T C by a hot reservoir and a cold reservoir, as in Fig. 18-18.
Let Q be the energy that is transferred as heat through the slab, from its hot face
to its cold face, in time t. Experiment shows that the conduction rate P cond (the
● The rate P cond at which energy is conducted through a slab
for which one face is maintained at the higher temperature
T H and the other face is maintained at the lower temperature
T C is
Here each face of the slab has area A, the length of the slab
(the distance between the faces) is L, and k is the thermal
conductivity of the material.
● Convection occurs when temperature differences cause an
energy transfer by motion within a fluid.
P cond ϭ
Q
t
ϭ kA
T H Ϫ T C
L
.
Key Ideas
● Radiation is an energy transfer via the emission of electromagnetic energy. The rate P rad at which an object emits
energy via thermal radiation is
P rad ϭ s´AT
4
,
where s (ϭ 5.6704 ϫ 10
Ϫ8
W/m
2 иK
4
) is the Stefan –
Boltzmann constant, ´ is the emissivity of the object’s surface, A is its surface area, and T is its surface temperature
(in kelvins). The rate P abs at which an object absorbs energy
via thermal radiation from its environment, which is at the
uniform temperature T env (in kelvins), is
P abs ϭ s´AT
4
env .
Figure 18-18 Thermal conduction. Energy is
transferred as heat from a reservoir at
temperature T H to a cooler reservoir at
temperature T C through a conducting slab
of thickness L and thermal conductivity k.
k
Hot reservoir
at T H
Cold reservoir
at T C
L
T C
T H >
Q
We assume a steady
transfer of energy as heat.
18-6 HEAT TRANSFER MECHANISMS
After reading this module, you should be able to . . .
18.31 For thermal conduction through a layer, apply the relationship between the energy-transfer rate P cond and the
layer’s area A, thermal conductivity k, thickness L, and
temperature difference ⌬T (between its two sides).
18.32 For a composite slab (two or more layers) that has
reached the steady state in which temperatures are no
longer changing, identify that (by the conservation of
energy) the rates of thermal conduction P cond through the
layers must be equal.
18.33 For thermal conduction through a layer, apply the
relationship between thermal resistance R, thickness L,
and thermal conductivity k.
18.34 Identify that thermal energy can be transferred by
convection, in which a warmer fluid (gas or liquid) tends to
rise in a cooler fluid.
18.35 In the emission of thermal radiation by an object, apply
the relationship between the energy-transfer rate P rad and
the object’s surface area A, emissivity ´, and surface temperature T (in kelvins).
18.36 In the absorption of thermal radiation by an object,
apply the relationship between the energy-transfer rate
P abs and the object’s surface area A and emissivity ´, and
the environmental temperature T (in kelvins).
18.37 Calculate the net energy-transfer rate P net of an object
emitting radiation to its environment and absorbing radiation from that environment.
Learning Objectives
CHAPTE R 18 TE M PE RATU R E, H EAT, AN D TH E FI RST L AW OF TH E R M ODYNAM ICS
Heat Transfer Mechanisms
We have discussed the transfer of energy as heat between a system and its environment, but we have not yet described how that transfer takes place. There are
three transfer mechanisms: conduction, convection, and radiation. Let’s next examine these mechanisms in turn.
Conduction
If you leave the end of a metal poker in a fire for enough time, its handle will get
hot. Energy is transferred from the fire to the handle by (thermal) conduction
along the length of the poker. The vibration amplitudes of the atoms and electrons of the metal at the fire end of the poker become relatively large because
of the high temperature of their environment. These increased vibrational amplitudes, and thus the associated energy, are passed along the poker, from atom to
atom, during collisions between adjacent atoms. In this way, a region of rising
temperature extends itself along the poker to the handle.
Consider a slab of face area A and thickness L, whose faces are maintained
at temperatures T H and T C by a hot reservoir and a cold reservoir, as in Fig. 18-18.
Let Q be the energy that is transferred as heat through the slab, from its hot face
to its cold face, in time t. Experiment shows that the conduction rate P cond (the
● The rate P cond at which energy is conducted through a slab
for which one face is maintained at the higher temperature
T H and the other face is maintained at the lower temperature
T C is
Here each face of the slab has area A, the length of the slab
(the distance between the faces) is L, and k is the thermal
conductivity of the material.
● Convection occurs when temperature differences cause an
energy transfer by motion within a fluid.
P cond ϭ
Q
t
ϭ kA
T H Ϫ T C
L
.
Key Ideas
● Radiation is an energy transfer via the emission of electromagnetic energy. The rate P rad at which an object emits
energy via thermal radiation is
P rad ϭ s´AT
4
,
where s (ϭ 5.6704 ϫ 10
Ϫ8
W/m
2 иK
4
) is the Stefan –
Boltzmann constant, ´ is the emissivity of the object’s surface, A is its surface area, and T is its surface temperature
(in kelvins). The rate P abs at which an object absorbs energy
via thermal radiation from its environment, which is at the
uniform temperature T env (in kelvins), is
P abs ϭ s´AT
4
env .
Figure 18-18 Thermal conduction. Energy is
transferred as heat from a reservoir at
temperature T H to a cooler reservoir at
temperature T C through a conducting slab
of thickness L and thermal conductivity k.
k
Hot reservoir
at T H
Cold reservoir
at T C
L
T C
T H >
Q
We assume a steady
transfer of energy as heat.
18-6 HEAT TRANSFER MECHANISMS
After reading this module, you should be able to . . .
18.31 For thermal conduction through a layer, apply the relationship between the energy-transfer rate P cond and the
layer’s area A, thermal conductivity k, thickness L, and
temperature difference ⌬T (between its two sides).
18.32 For a composite slab (two or more layers) that has
reached the steady state in which temperatures are no
longer changing, identify that (by the conservation of
energy) the rates of thermal conduction P cond through the
layers must be equal.
18.33 For thermal conduction through a layer, apply the
relationship between thermal resistance R, thickness L,
and thermal conductivity k.
18.34 Identify that thermal energy can be transferred by
convection, in which a warmer fluid (gas or liquid) tends to
rise in a cooler fluid.
18.35 In the emission of thermal radiation by an object, apply
the relationship between the energy-transfer rate P rad and
the object’s surface area A, emissivity ´, and surface temperature T (in kelvins).
18.36 In the absorption of thermal radiation by an object,
apply the relationship between the energy-transfer rate
P abs and the object’s surface area A and emissivity ´, and
the environmental temperature T (in kelvins).
18.37 Calculate the net energy-transfer rate P net of an object
emitting radiation to its environment and absorbing radiation from that environment.
Learning Objectives