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Can improved engineering and materials be employed in heat engines to reduce heat transfer into the environment? Can they eliminate heat transfer into the environment entirely?

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Does the second law of thermodynamics alter the conservation of energy principle?

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Problem exercises

A certain gasoline engine has an efficiency of 30.0%. What would the hot reservoir temperature be for a Carnot engine having that efficiency, if it operates with a cold reservoir temperature of 2 00 º C size 12{2"00"°C} {} ?

403 º C size 12{"403"°C} {}

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A gas-cooled nuclear reactor operates between hot and cold reservoir temperatures of 700 º C size 12{"700"°C} {} and 27 . 0 º C size 12{"27" "." 0°C} {} . (a) What is the maximum efficiency of a heat engine operating between these temperatures? (b) Find the ratio of this efficiency to the Carnot efficiency of a standard nuclear reactor (found in [link] ).

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(a) What is the hot reservoir temperature of a Carnot engine that has an efficiency of 42.0% and a cold reservoir temperature of 27 . 0 º C size 12{"27" "." 0°C} {} ? (b) What must the hot reservoir temperature be for a real heat engine that achieves 0.700 of the maximum efficiency, but still has an efficiency of 42.0% (and a cold reservoir at 27 . 0 º C size 12{"27" "." 0°C} {} )? (c) Does your answer imply practical limits to the efficiency of car gasoline engines?

(a) 2 44 º C size 12{2"44"°C} {}

(b) 477 º C size 12{"477"°C} {}

(c)Yes, sinceautomobiles enginescannot gettoo hotwithout overheating,their efficiencyis limited.

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Steam locomotives have an efficiency of 17.0% and operate with a hot steam temperature of 425 º C size 12{"425"°C} {} . (a) What would the cold reservoir temperature be if this were a Carnot engine? (b) What would the maximum efficiency of this steam engine be if its cold reservoir temperature were 150 º C size 12{"150"°C} {} ?

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Practical steam engines utilize 450 º C size 12{"450"°C} {} steam, which is later exhausted at 270 º C size 12{"270"°C} {} . (a) What is the maximum efficiency that such a heat engine can have? (b) Since 270 º C size 12{"270"°C} {} steam is still quite hot, a second steam engine is sometimes operated using the exhaust of the first. What is the maximum efficiency of the second engine if its exhaust has a temperature of 150 º C size 12{"150"°C} {} ? (c) What is the overall efficiency of the two engines? (d) Show that this is the same efficiency as a single Carnot engine operating between 450 º C size 12{"450"°C} {} and 150 º C size 12{"150"°C} {} . Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics .

(a) Eff 1 = 1 T c,1 T h,1 = 1 543 K 723 K = 0 . 249 or 24 . 9% size 12{ ital "Eff" rSub { size 8{1} } =1 - { {T rSub { size 8{"c,1"} } } over {T rSub { size 8{"h,1"} } } } =1 - { {"543 K"} over {"723 K"} } =0 "." "249"`"or"`"24" "." 9%} {}

(b) Eff 2 = 1 423 K 543 K = 0 . 221 or 22 . 1% size 12{ ital "Eff" rSub { size 8{2} } =1 - { {"423 K"} over {"543 K"} } =0 "." "221"`"or"`"22" "." 1%} {}

(c) Eff 1 = 1 T c,1 T h,1 T c,1 = T h,1 1 eff 1 similarly, T c,2 = T h,2 1 Eff 2 using T h,2 = T c,1 in above equation gives T c,2 = T h,1 1 Eff 1 1 Eff 2 T h,1 1 Eff overall 1 Eff overall = 1 Eff 1 1 Eff 2 Eff overall = 1 1 0 . 249 1 0 . 221 = 41 . 5% alignl { stack { size 12{ ital "Eff" rSub { size 8{1} } =1 - { {T rSub { size 8{"c,1"} } } over {T rSub { size 8{"h,1"} } } } drarrow T rSub { size 8{"c,1"} } =T rSub { size 8{"h,1"} } left (1 - ital "eff" rSub { size 8{1} } right )} {} #"similarly",`T rSub { size 8{"c,2"} } =T rSub { size 8{"h,2"} } left (1 - ital "Eff" rSub { size 8{2} } right ) {} # "using"`T rSub { size 8{"h,2"} } =T rSub { size 8{"c,1"} } `"in"`"above"`"equation"`"gives" {} #T rSub { size 8{"c,2"} } =T rSub { size 8{"h,1"} } left (1 - ital "Eff" rSub { size 8{1} } right ) left (1 - ital "Eff" rSub { size 8{2} } right ) equiv T rSub { size 8{"h,1"} } left (1 - ital "Eff" rSub { size 8{"overall"} } right ) {} # ∴` left (1 - ital "Eff" rSub { size 8{"overall"} } right )= left (1 - ital "Eff" rSub { size 8{1} } right ) left (1 - ital "Eff" rSub { size 8{2} } right ) {} #ital "Eff" rSub { size 8{"overall"} } =1 - left (1 - 0 "." "249" right ) left (1 - 0 "." "221" right )="41" "." 5% {} } } {}

(d) Eff overall = 1 423 K 723 K = 0 . 415 or 41 . 5% size 12{ ital "Eff" rSub { size 8{"overall"} } =1 - { {"423 K"} over {"723 K"} } =0 "." "415"`"or"`"41" "." 5%} {}

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A coal-fired electrical power station has an efficiency of 38%. The temperature of the steam leaving the boiler is 550 º C size 12{"550"°C} {} . What percentage of the maximum efficiency does this station obtain? (Assume the temperature of the environment is 20 º C size 12{"20"°C} {} .)

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Would you be willing to financially back an inventor who is marketing a device that she claims has 25 kJ of heat transfer at 600 K, has heat transfer to the environment at 300 K, and does 12 kJ of work? Explain your answer.

The heat transfer to the cold reservoir is Q c = Q h W = 25 kJ 12 kJ = 13 kJ size 12{Q rSub { size 8{c} } =Q rSub { size 8{h} } - W="25"`"kJ" - "12"`"kJ"="13"`"kJ"} {} , so the efficiency is Eff = 1 Q c Q h = 1 13 kJ 25 kJ = 0 . 48 size 12{ ital "Eff"=1 - { {Q rSub { size 8{c} } } over {Q rSub { size 8{h} } } } =1 - { {"13"`"kJ"} over {"25"`"kJ"} } =0 "." "48"} {} . The Carnot efficiency is Eff C = 1 T c T h = 1 300 K 600 K = 0 . 50 size 12{ ital "Eff" rSub { size 8{C} } =1 - { {T rSub { size 8{c} } } over {T rSub { size 8{h} } } } =1 - { {"300"`K} over {"600"`K} } =0 "." "50"} {} . The actual efficiency is 96% of the Carnot efficiency, which is much higher than the best-ever achieved of about 70%, so her scheme is likely to be fraudulent.

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Unreasonable Results

(a) Suppose you want to design a steam engine that has heat transfer to the environment at 270ºC and has a Carnot efficiency of 0.800. What temperature of hot steam must you use? (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?

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Unreasonable Results

Calculate the cold reservoir temperature of a steam engine that uses hot steam at 450 º C size 12{"450"°C} {} and has a Carnot efficiency of 0.700. (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?

(a) –56.3ºC

(b) The temperature is too cold for the output of a steam engine (the local environment). It is below the freezing point of water.

(c) The assumed efficiency is too high.

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Questions & Answers

how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
the range of objects and phenomena studied in physics is
Bethel Reply
what is Linear motion
Hamza Reply
straight line motion is called linear motion
then what
Amera
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
your are wrong Saeedul
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions. 
Praise
what is a classical electrodynamics?
Marga
what is dynamics
Marga
dynamic is the force that stimulates change or progress within the system or process
Oze
what is the formula to calculate wavelength of the incident light
David Reply
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
Hassan Reply
State the forms of energy
Samzy Reply
machanical
Ridwan
Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
Clement Reply
correct
Akinpelu
what is mechanical wave
Akinpelu Reply
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
Samuel Reply
watt
Okoli
Am I correct
Okoli
it can be in kilowatt, megawatt and so
Femi
yes
Femi
correct
Jaheim
kW
Akinpelu
OK that's right
Samuel
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
What is physics
aish Reply
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
Syafiqah Reply
reasonable
Femi
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
What is a wave
Mutuma Reply
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
mistakes thanks
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k
Favour Reply
Difference between north seeking pole and south seeking pole
Stanley Reply
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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