Notes added after lecture:
• In class we derived the molar specific heats for an ideal monatomic gas
at constant pressure and at constant volume (see p. 621-623) and
showed that:
C P C =VR
See Table 18-3 to compare with experiment. We can also look at the
molar specific heats of diatomic and tri-atomic gases, using
experimental data listed in Table 20-1 of Giancoli’s book “General
Physics”. The next slide shows selected entries from that table. Note
that the units are in (cal/mol.-K) instead of the usual (J/mol.-K). The
ratio of the heat capacities is important because it determines the slope
of adiabatic curves on the P-V diagram for the gas. This ratio is usually
labeled γ (Greek letter “gamma”). For monatomic gases, γ = C /C =
P V
5/3 = 1.67 , since CV=(3/2)R and C =P5/2)R.
For diatomic gases, γ = (7/5) = 1.40, since C V(5/2)R and C =(P/2)R
due to the two additional rotational degrees of freedom. For CO the
value of γ is 1.30, since it is a tri-atomic molecule. 2 o
Molar Heat Capacities of Gases at 15 C
Gas CVcal/ CP CP-CV γ
mol•K
cal/mol•K cal/mol•K
He 2.98 4.97 1.99 1.67
Ne 2.98 4.97 1.99 1.67
N 2 4.96 6.95 1.99 1.40
O 2 5.03 7.03 2.00 1.40
CO 6.80 8.83 2.03 1.30
2 The Laws of Thermodynamics
Specific Heats, 2nd Law, Heat
Engines, Carnot Cycle,
Refrigerators Specific Heats for a Monatomic Ideal Gas:
Constant Pressure, Constant Volume
The P-V curve for an adiabat is
given by
where The Second Law of Thermodynamics
We observe that heat always flows
spontaneously from a warmer object to a
cooler one, although the opposite would not
violate the conservation of energy. This
direction of heat flow is one of the ways of
expressing the second law of
thermodynamics:
When objects of different temperatures are brought
into thermal contact, the spontaneous flow of heat
that results is always from the high temperature
object to the low temperature object. Spontaneous
heat flow never proceeds in the reverse direction. Heat Engines and the Carnot Cycle
A heat engine is a device that converts heat into
work. A classic example is the steam engine.
Fuel heats the water; the vapor expands and
does work against the piston; the vapor
condenses back
into water again
and the cycle
repeats. Heat Engines and the Carnot Cycle
All heat engines have:
• a high-temperature reservoir
• a low-temperature reservoir
• a cyclical engine
These are illustrated
schematically here. Heat Engines and the Carnot Cycle
An amount of heat Q ishsupplied from the hot
reservoir to the engine during each cycle. Of that
heat, some appears as work, and the rest, Q , isc
given off as waste heat to the cold reservoir.
The efficiency is the fraction of the heat
supplied to the engine that appears as work. Heat Engines and the Carnot Cycle
The efficiency can also be written:
In order for the engine to run, there must
be a temperature difference; otherwise
heat will not be transferred. Heat Engines and the Carnot Cycle
The maximum-efficiency heat engine is
described in Carnot’s theorem:
If an engine operating between two constant-
temperature reservoirs is to have maximum
efficiency, it must be an engine in which all processe
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