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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

Can you please help me with some questions
Janet Reply
topic-- question
Salman
I know this is unrelated to physics, but how do I get the MCQs and essay to work. they arent clickable.
Jake Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian Reply
why is a body moving at a constant speed able to accelerate
Lilian Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian
because it changes only direction and the speed is kept constant
Justice
Why is the sky blue...?
Star Reply
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
Mike
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
fasawe Reply
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Azummiri Reply
Be raised until its distance from d lens is 27cm find d radius of curvature
Azummiri
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
FlAsH Reply
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
Fatinizzah Reply
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
Ramonyai
why is the north side is always referring to n side of magnetic
sam Reply
who is a nurse
Chilekwa Reply
A nurse is a person who takes care of the sick
Bukola
a nurse is also like an assistant to the doctor
Gadjawa
explain me wheatstone bridge
Malik Reply
good app
samuel
Wheatstone bridge is an instrument used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
MUHD
Rockwell Software is Rockwell Automation’s "Retro Encabulator". Now, basically the only new principle involved is that instead of power being generated by the relative motion of conductors and fluxes, it’s produced by the modial interaction of magneto-reluctance and capacitive diractance. The origin
Chip
what refractive index
Adjah Reply
write a comprehensive note on primary colours
Harrison Reply
relationship between refractive index, angle of minimum deviation and angle of prism
Harrison
Who knows the formula for binding energy,and what each variable or notation stands for?
Agina 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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