Peoples Physics Concepts

18.4. Heat Engine http://www.ck12.org

Gas Heat Engines

• When gas pressure-forces are used to move an object then work is done on the object by the expanding gas.
  Work can be done on the gas in order to compress it.


• If you plot pressure on the vertical axis and volume on the horizontal axis, the work done in any complete
  cycle is the area enclosed by the graph. For a partial process, work is the area underneath the curve, orP∆V.

Example 1

Question:A heat engine operates at a temperature of 650K. The work output is used to drive a pile driver, which is

a machine that picks things up and drops them. Heat is then exhausted into the atmosphere, which has a

temperature of 300K.

a) What is the ideal efficiency of this engine?

b) The engine drives a 1200kg weight by lifting it 50min 2. 5 sec. What is the engine’s power output?

c) If the engine is operating at 50% of ideal efficiency, how much power is being consumed?

d) How much power is exhausted?

e) The fuel the engine uses is rated at 2. 7 × 106 J/kg. How many kg of fuel are used in one hour?

Answer:

a) We will plug the known values into the formula to get the ideal efficiency.

η= 1 −

Tcold

T

hot=1-300K650K=54%

b) To find the power of the engine, we will use the power equation and plug in the known values.

P=

W

t

=

F d

t

=

mad

t

=

1200kg× 9 .8m/s^2 ×50m

2 .5sec

=240kW

c) First, we know that it is operating at 50% of ideal efficiency. We also know that the max efficiency of this engine
is 54%. So the engine is actually operating at

. 5 ×54%=27%

of 100% efficiency. So 240kW is 27% of what?

. 27 x=240kW⇒x=

240kW

. 27
=890kW

d) Since we know how much power is being put into the engine and how much energy is actually being used to lift

the weight, we can determine how much energy is not actually being used to do work.