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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

find the density of a fluid in which a hydrometer having a density of 0.750g/mL floats with 92.0% of its volume submerged.
Neshrin Reply
Uniform speed
Sunday
(a)calculate the buoyant force on a 2.00-L Helium balloon.(b) given the mass of the rubber in the balloon is 1.50g. what is the vertical force on the balloon if it is let go? you can neglect the volume of the rubber.
Neshrin Reply
To Long
Usman
pleaseee. can you get the answer? I can wait till 12
Neshrin
a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
Bala Reply
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
Emmanuel Reply
What's sup guys
Peter
cul and you all
Okeh
cool you bro
Nana
so what is going on here
Nana
hello peeps
Joseph
Michelson Morley experiment
Riya Reply
how are you
Naveed
am good
Celine
you
Celine
hi
Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
Emmanuel Reply
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
thanks jare
Doc
Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
AMADI
what is physic
zalmia Reply
please gave me answar
zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
Okay
William
hi sir
Bala
how easy to understanding physics sir
Bala
Easy to learn
William
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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