Physics 207
Homework Set #6
1) In every cycle, a heat engine absorbs 2000 J from a hot reservoir at 700K, does
800 J of work. The waste heat is expelled into a cold reservoir at 300K. a) How
much heat is expelled into the cold reservoir in each cycle? b) What is the
efficiency of the engine? c) What would be the efficiency of the “best possible”
heat engine working between these two temperature reservoirs?
a) Qc = Qh-W = 2000J – 800J =1200J
b) e =W/Qh = 800J/2000J = 0.4
c) ecarnot = 1-Tc/Th = 1-300/700 = 400/700 = 0.57
2) Why is it that a heat engine can never have and efficiency of one, i.e. why can’t
we convert all heat into work?
Heat is the random kinetic energy of the particles. The only way to convert
all heat into work would be if all of the particles were moving together in
on direction. This will never happen.
3) Breifly describe the three basic heat transfer mechanisms.
Conduction is the transfer of heat energy without transfering mass
Convection is the transfer of heat energy in conjuction with the transfer of
mass
Radiation is the transfer of energy by “light”. It takes place even in a
vacuum.
4) Perform the following temperature conversions. a) Convert 68F into Celsius.
(Room Temperature) b) Convert -40C into Fahrenheit. c) Convert 0 K into
Fahrenheit.(Absolute zero. Hint: convert to Celsius first). Convert 37C into
Fahrenheit?
a) 68F = (5/9)(68-32) = 20C
b) -40C = (9/5)(-40) + 32 = -40F
c) 0K = -273C = (9/5)(-273) + 32 =-459F
d) 37C = (9/5)(37) +32 = 98.6F
5) There are approximately 3.4 ×1023 kg of water in the ocean. a)How many Joules
of energy would it take to raise the temperature of the ocean 1C? b) Given that
the power output of all of the electric power plants in the world is approximately
2×1012W, how long (in seconds) would it take to generate this much energy? c)
How long is this in years? (A rise in ocean temperatures of this magnitude is the
kind of effect we would expect from global warming.)
a) Q=mCT = (3.4 ×1023 kg)(4186 J/kgC)( 1C) =1.42×1027J.
b) Power=energy/time
time = energy/power = (1.42×1027J)/( 2×1012W) = 7.12×1014s
 1hr  1day  1yr 
  2.26 107 yr
c) 7.12 1014 s
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 3600s  24hr  365day 