Page 244 - Standard Handbook Of Petroleum & Natural Gas Engineering

Thermodynamics 217

The second law yields

(2-124)

To obtain the fraction of the heat input Q, that is converted to useful work, Equa-
tions 2-123 and 2-124 are combined to give
Ti-T,
W
_- (2-125)
--
Qi Ti
This important result is called the Curnot engine efficiency and yields the maximum
thermal efficiency that can be achieved by any heat engine cycle operating between any
two given temperature limits. Heat engines have been proposed to operate within
the temperature gradients of the ocean as a means of harnessing the vast amounts of
renewable energy available from that source.
Heat Pumps
A heat pump, which is the opposite of a heat engine, uses work energy to transfer
heat from a cold reservoir to a “hot” reservoir. In households, the cold reservoir is
often the surrounding air or the ground while the hot reservoir is the home. For an
ideal heat pump system with Q1 and TI referring to the hot reservoir and Qr and T2
referring to the cold reservoir, the work required is, from the first and second laws,

(2-126)

Application of this result shows that if 100 units of heat Q, are needed to maintain a
household at 24°C (297°K) by “pumping” heat from the outside surroundings at 0°C
(273”K), it would require a minimum of (24 x 100/297) = 8.08 units of work energy.

Refrigeration Machines
Refrigerating machines absorb heat Q from a cold reservoir at temperature T,,
and discharge heat Q,, into a “hot” reservoir at Ti. To accomplish this, work energy
must also be absorbed. The minimum required work is obtained as shown before,
using the first and second laws:

W - Ti -T,
Q, Ti (2-127)

Reversible Work of Expansion or Compression

Many systems involve only work of expansion or compression of the system
boundaries. For such systems the first law is written for unit mass of fluid as the basis:
dU = SQ - PdV (2-128)
where s,”’ P dV represents the reversible work of compression or expansion.