http://www.ck12.org Chapter 19. Thermodynamics and Heat Engines
ec= 1 −
Tc
Th[7] Efficiency of a Carnot (ideal) heat enginewhereTcandThare the temperatures of the hot and cold reservoirs, respectively.
Some Important Points
- In a practical heat engine, the change in internal energy must be zero over a complete cycle. Therefore, over
a complete cycleW=∆Q. - The work done by a gas during a portion of a cycle =P∆V, note∆Vcan be positive or negative.
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 (seeP−Vdiagrams in the last
chapter), 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.
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) 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
Thot=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