Chapter 15 Learning ObjectivesConcepts and Skills to Review
Internal energy and heat (Sections 14.1-14.2)
System and environment (Section 14.1)
Area under a graph (Section 3.2)
Work done is the area under a graph of F(x) (Section 6.4)
Specific heat of ideal gases at constant volume (Section 14.4)
Natural logarithm (Appendix A.3)
Summary
The first law of thermodynamics is a statement of energy conservation:
ΔU = Q – W
(15-1)
where Q is the heat flow into the system and W is the work done by the system.
Pressure, temperature, volume, number of moles, internal energy, and entropy are state variables; they describe the state of a system at some instant of time but not how the system got to that state. Heat and work are not state variables—they describe how a system gets from one state to another.
The work done by a system when the pressure is constant—or for a volume change small enough that the pressure change is insignificant-is:
W = PΔV
(15-2)
In general, the work done is the total area under the PV curve.
The change in internal energy of an ideal gas is determined solely by the temperature change. Therefore
ΔU = 0 (ideal gas, isothermal)
(15-7)
A process in which no heat is transferred into or out of the system is called an adiabatic process.
The molar specific heats of an ideal gas at constant volume and constant pressure are related by
Cv = Cp – R
(15-11)
Heat flow from a hotter body to a colder body is always irreversible.
For a cyclical engine, heat pump, etc., since ΔU = 0 for a cycle, conservation of energy requires
Q = QH + QC = W
The efficiency of an engine (or the inefficiency of a heat pump, refrigerator, or air conditioner) is defined as
A reservoir is a system with such a large heat capacity that it can exchange heat in either direction with a negligibly small temperature change.
The second law of thermodynamics can be stated in various equivalent ways: (1) heat never flows spontaneously from a colder body to a hotter body, (2) no engine can have 100% efficiency, (3) no engine can have an efficiency greater than the inefficiency of any heat pump operating between the same hot and cold reservoirs, (4) no heat pump (or refrigerator) can have an inefficiency of zero, (5) every engine has ee ≤ er and every heat pump has ep ≥ er, (6) the entropy of the universe never decreases.
The efficiency of reversible engine is determined only by the absolute temperatures of the hot and cold reservoirs:
