Conceptual Physics

(Sean Pound) #1

21.1 - Efficiency


Efficiency: The ratio of the net work done by an


engine during a cycle to the heat energy


supplied to the engine.


Engine design has been refined for hundreds of years, as engineers have sought to
increase the power and reliability of engines while decreasing their size. Equally
importantly, they have sought to increase the efficiency of engines, the amount of useful
work an engine does divided by the amount of thermal energy supplied to it.
The first formula in Equation 1 states the definition of the efficiency of a heat engine.
The efficiency equals the net work W done by the engine divided by the heat Qh
transferred to the system from the hot reservoir. This ratio is often stated as a
percentage. A typical internal combustion automobile engine has an efficiency of about
25%, while the diesel and coal powered engines in electrical plants have efficiencies
ranging from 40% to 60%. These numbers are for the engines alone. The overall
systemsí the entire car, the whole electrical plant í run at lower total efficiencies due
to inefficiencies outside the engines.
The second formula for engine efficiency shown in Equation 1 provides a way to
calculate engine efficiency from the heat Qh added to the engine, and the heat Qc that
flows out.
The second equation for engine efficiency is derived below from the definition (the first
equation). The derivation uses the first law of thermodynamics: The net heat flow
equals the work done by the engine plus its change in internal energy. Since the
internal energy of an engine is the same at the beginning and end of a cycle, the net
heat flow equals the work done by the engine.

Engine efficiency


e = W/Qh


e = engine efficiency


W = net work during engine cycle


Qh = heat in during cycle


Qc = heat out during cycle


What is the efficiency of this


engine?


e = 1 í (4700 J)/(8400 J)


e = 0.44 = 44%


Step Reason


1. e = W/Qh definition of efficiency


2. W = Qh – Qc first law of thermodynamics


3. substitute equation 2 into equation 1


4. divide


21.2 - Second law of thermodynamics


Second law of thermodynamics: No heat engine


can transform 100% of the energy supplied to it


into work during a cycle.


There are several equivalent ways to express the second law of thermodynamics. The
definition above states the law in a form that is one of its important consequences:
There is a limit to the amount of work that can be done by a heat engine supplied with a
certain amount of energy during a cycle. This is called the Kelvin-Planck statement of
the second law.
To take a step back for a moment: The first law of thermodynamics states that the net
heat transferred to a system equals the net work done by the system plus the change in
its internal energy. That provides one limit to how much work an engine can do: no
more than the net heat transferred to it. In essence, the first law is about energy

Second law of thermodynamics


Engines cannot transform 100% of heat
into work during a cycle

(^384) Copyright 2007 Kinetic Books Co. Chapter 21

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