2.4. THE SECOND LAW OF THERMODYNAMICS.
ENTROPY
• Heat engine efficiency:
(2.4a)
where Q1 is the heat obtained by the working substance, if); is the heat released
by the working substance.
• Efficiency of a Carnot cycle:
_ -r2
(2.4b)
'
where T1 and T2 are the temperatures of the hot and cold bodies respectively.
• Clausius inequality:
(2
(2.4c)
where 6Q is the elementary amount of heat transferred to the system (6Q is an
algebraic quantity).
• Entropy increment of a system:
AS
.
(2.4d)
• Fundamental relation of thermodynamics:
T dS
dU
p dV.
(2.4e)
• Relation between the entropy and the statistical weight SZ (the thermodynamic probability):
S = k In 52,
(2.4f)
where k is the Boltzmann constant.
2.113. In which case will the efficiency of a Carnot cycle be higher:
when the hot body temperature is increased by AT, or when the cold
body temperature is decreased by the same magnitude?
2.114. Hydrogen is used iu a Carnot cycle as a working substance.
Find the efficiency of the cycle, if as a result of an adiabatic expansion
(a) the gas volume increases n = 2.0 times;
(b) the pressure decreases n = 2.0 times.
2.115. A heat engine employing a Carnot cycle with an efficiency
of i = 10% is used as a refrigerating machine, the thermal reservoirs
being the same. Find its refrigerating efficiency E.
2.116. An ideal gas goes through a cycle consisting of alternate
isothermal and adiabatic curves (Fig. 2.2). The isothermal processes
proceed at the temperatures T1, T2, and T3. Find the efficiency of
such a cycle, if in each isothermal expansion the gas volume increases
in the same proportion.
2.117. Find the efficiency of a cycle consisting of two isochoric
and two adiabatic lines, if the volume of the ideal gas changes
n = 10 times within the cycle. The working substance is nitrogen.
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