Thermal Behavior of Matter and Heat Engines - Department of ...

When we stated the second law of thermodynamics,
we said that the spontaneous flow of heat is always
from high temperature to low temperature. The key
word here is “spontaneous”. It is possible for heat to
flow “uphill”, from a cold object to a hot one, but it
doesn’t happen spontaneously - work must be done
on the system to make it happen, just as work must
be done to pump water from a well. Refrigerators, air
conditioners, heat pumps are devices that use work
to make heat flow against its natural tendency.
By energy conservation, we have Q
= Q W .
h c
+
We define the coefficient of performance, COP, for a
refrigerator as an indicator of its effectiveness:
Qc
COP = .
W
Typical values for COP are in the range 2 to 6.
A heat pump can be considered as an air conditioner with the reservoirs switched. A
heat pump does a work W to remove an amount of heat from the cold reservoir of
outdoor air, then exhausts a heat Q h into the hot reservoir of air in the room. Just as
with the refrigerator and the air conditioner, the heat going to the hot reservoir is
Q
= Q W .
h c
+
In an ideal, reversible heat pump, we have
Q
c
T =
c holds, just as it does for a heat
engine. Thus, if you want to add a heat Q h to a room, the work that must be done to
accomplish this is
⎛ Q ⎞ ⎛ ⎞
= − =
⎜ −
c
T
⎟ =
⎜ −
c
W Q
⎟
h
Qc
Qh
1 Qh
1 .
⎝ Qh
⎠ ⎝ Th
⎠
Example
An ideal heat pump, one that satisfies the Carnot relation, is used to heat a room that
is at 293 K. If the pump does 275 J of work, how much heat does it supply to the
room if the outdoor temperature is (a) 273 K or (b) 263 K?
Q
h
T
h
18