Discussion Questions
A In this discussion question, you’ll think about a car engine in terms of
thermodynamics. Note that an internal combustion engine doesn’t fit very
well into the theoretical straightjacket of a heat engine. For instance, a
heat engine has a high-temperature heat reservoir at a single well-defined
temperature,TH. In a typical car engine, however, there are several very
different temperatures you could imagine using forTH: the temperature
of the engine block (∼ 100 ◦C), the walls of the cylinder (∼ 250 ◦C), or the
temperature of the exploding air-gas mixture (∼ 1000 ◦C, with significant
changes over a four-stroke cycle). Let’s useTH∼ 1000 ◦C.
Burning gas supplies heat energyQHto your car’s engine. The engine
does mechanical workW, but also expels heatQLinto the environment
through the radiator and the exhaust. Conservation of energy gives
QH=QL+W,
and the relative proportions ofQLandWare usually about 90% to 10%.
(Actually it depends quite a bit on the type of car, the driving conditions,
etc.) Here,QH,QL, andWare all positive according to the sign conven-
tion defined on p. 315.
(1) A gallon of gas releases about 140 MJ of heatQHwhen burned. Es-
timate the change in entropy of the universe due to running a typical car
engine and burning one gallon of gas. Note that you’ll have to introduce
appropriate plus and minus signs, as defined in the relation∆S=Q/T,
in which heat input raises an object’s entropy and heat output lowers it.
(You’ll have to estimate how hot the environment is. For the sake of ar-
gument, assume that the work done by the engine,W, remains in the
form of mechanical energy, although in reality it probably ends up being
changed into heat when you step on the brakes.) Is your result consistent
with the second law of thermodynamics?
(2)QLis obviously undesirable: you pay for it, but all it does is heat the
neighborhood. Suppose that engineers do a really good job of getting
rid of the effects that createQL, such as friction. CouldQLever be re-
duced to zero, at least theoretically? What would happen if you redid the
calculation in #1, but assumedQL= 0?
B When we run the Carnot engine in figures d-g, there are four parts
of the universe that undergo changes in their physical states: the hot
reservoir, the cold reservoir, the working gas, and the outside world to
which the shaft is connected in order to do physical work. Over one full
cycle, discuss which of these parts gain entropy, which ones lose entropy,
and which ones keep the same entropy. During which of the four strokes
do these changes occur?5.4 Entropy as a microscopic quantity
5.4.1 A microscopic view of entropy
To understand why the second law of thermodynamics is always
true, we need to see what entropy really means at the microscopic
level. An example that is easy to visualize is the free expansion of
a monoatomic gas. Figure a/1 shows a box in which all the atoms
of the gas are confined on one side. We very quickly remove the326 Chapter 5 Thermodynamics