Conceptual Physics

efficiency. Next, calculate how much heat needs to be added to the engine for it to perform the desired amount of work. The gasoline is the

source of the added heat. To find out how much gasoline to add, you need to know that one liter of gasoline generates 1.30×10^8 J of heat

when combusted in the engine.

The correct amount of gasoline will be under a tenth of a liter. Calculate the amount

of gasoline needed to reach 90.0 km/h to three significant digits (to a ten-thousandth

of a liter), enter this value, and press GO to see the results. Press RESET to try

again.

If you want, you could calculate the kinetic energy of the car at the final speed and

determine what percent of the work goes to overcoming resistive forces versus

increasing the KE of the car. (The mass of the car is 1280 kg.)

If you have trouble getting the right answer, see the section on engine efficiency.

21.13 - Gotchas

Using Celsius temperatures. All the equations in this chapter that contain a temperature factor require the temperature to be in Kelvin.

My friend has an engine that is 101% efficient. This is not possible: It contradicts the second law of thermodynamics. It also contradicts the first

law. Making that claim probably breaks some FTC regulations too.

If I clean my room, it will become more ordered and I will be breaking the second law of thermodynamics. Not to dissuade you from cleanliness,

but you are not breaking the law. Your room is not an isolated system; other parts of the system (like the molecules within your body) have

become more disordered.

21.14 - Summary

The efficiency of a heat engine is the ratio of the net work it does divided by heat

added during an engine cycle. There are several equivalent statements of the

second law of thermodynamics. One states that no heat engine can transform 100%

of the thermal energy supplied to it during a cycle into work.

Entropy is a property of a system. Entropy increases as heat is transferred into the

system. The change in entropy can be calculated as the heat transferred during a

reversible process (one in which the system can be returned to its initial state

without additional energy) divided by the temperature. Another way to state the

second law is that in any isolated system í such as the universe í entropy never

decreases.

The maximum efficiency possible for any heat engine depends on the ratio of the

temperatures of the cold and hot reservoirs. The greater the difference in

temperatures, the lower the ratio and the more efficient the engine can be. A Carnot

engine is a theoretical engine that achieves this maximum efficiency.

The internal combustion engine in most automobiles utilizes the Otto cycle. The

efficiency of the internal combustion engine depends on the compression ratio, the

ratio of the maximum to minimum gas volume in the engine.

Heat pumps can be used instead of furnaces to warm buildings. Unlike a heat

engine, a heat pump uses work to transfer heat from the cool reservoir (outdoors) to

the hot reservoir (the building interior). Just as we rated heat engines by their

efficiency, for a heat pump the analogous quantity is its coefficient of performance.

A heat pump’s coefficient of performance increases when the difference in

temperature between the hot and cold reservoirs decreases.

Efficiency

e = W/Qh

Entropy

In an isolated system, ǻS• 0

Coefficient of performance

(^396) Copyright 2007 Kinetic Books Co. Chapter 21