Essential University Physics, 3e (Wolfson) 3e (Wolfson) Chapter 16 Te Temperature mperature and Heat
1 6. 1 Co nc e pt ua lQue s t i o ns 1) It is a well-known fact that water has a higher specific heat than iron. Now, consider equal masses of water and iron that are initially in thermal equilibrium. The same amount of heat, ! calories, is added to each one. "hich statement is true# $) They remain in thermal equilibrium. %) They are no longer in thermal equilibrium& the iron is warmer. ') They are no longer in thermal equilibrium& the water is warmer. () It is impossible to say without knowing the eact mass in*ol*ed. +) It is impossible to say without knowing the eact specific heats. $nswer % ar 1
) $ thermally isolated system is made up of a hot piece of aluminum and a cold piece p iece of copper& the aluminum and the copper are in thermal contact. The specific heat of aluminum is more than double that of copper. "hich ob/ect eperiences the greater temperature change during the time the system takes to reach thermal equilibrium# $) The copper eperiences a greater temperature change. %) The aluminum eperiences a greater temperature change. ') Neither& both ob/ects eperience the same magnitude temperature change. () It is impossible to tell without knowing the masses. +) It is impossible to tell without knowing the *olumes. $nswer ( ar 1
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) $n architect is interested in estimating the heat loss 3in kcal4s) through a sheet of insulating material as a function of the thickness of the sheet. $ssuming fied temperatures on the two faces of the sheet, which one of the graphs in the figure best represents the rate of heat transfer as a function of the thickness of the insulating sheet#
$) $ %) % ') ' () ( +) + $nswer ' ar 1
1 6 . 2 Pr o bl e ms 1) 3a) Internal human body temperature is often stated to be normal at 56.78. "hat is this temperature on the 'elsius and 9el*in scales# 3b) :allium boils at !;7'. "hat is the corresponding temperature in the 8ah renheit and 9el*in scales# 3c) The boiling point of liquid nitrogen is <<.! 9. "hat is the corresponding temperature in the 8ahrenheit and 'elsius scales# $nswer 3a) <.!7', 1! 9 3b) =!!178, =<6 9 3c) -178, -157' ar 1
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) It is necessary to determine the specific heat of an unknown ob/ect. The mass of the ob/ect is measured to be 155.! g. It is determined eperimentally that it takes 1.! > to raise the temperature 1!.!7'. 8ind the specific heat of the ob/ect. $) 6.!= >4kg ? 9 %) 1!! >4kg ? 9 ') !.!!1! >4kg ? 9 () .16 @ 1! >4kg ? 9 $nswer $ ar 1
) $ =6-g empty iron kettle is put on a sto*e. Aow much heat. in /oules. must it absorb to raise its temperature from to 3The specific heat for iron is 11 cal4kgB'7, 1 cal C =.15! >) $) <=! > %) 11,!! > ') 11! > () 1,1!! > $nswer $ ar ;!D
=) If we use < " of power to heat 1=6 g of water, how long will it take to raise the temperature of the water from 1;7' to ;7'# The specific heat of water is =15! >4kgB9. $) 5 s %) ;. s ') s () 11= h $nswer $ ar 1
;) $ 5!;-g meteor impacts the earth at a speed of 15 m4s. If all of its energy is entirely con*erted to heat in the meteor, what will be the resulting temperature rise of the meteor, assuming it does not melt# The specific heat for the meteor material is =< >4kg?9, which is about the same as that of iron. $) 61!7' %) ,;=!,!!!7' ') .1!7' () 11,
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) $ person pours ! g of water at =;7' into an 6;;-g aluminum container with an initial temperature of 1!7'. The specific heat of aluminum is 5!! >43kg?9) and that of water is =15! >4 3kg?9). "hat is the final temperature of the system, assuming no heat is echanged with the surroundings# $) 67' %) 7' ') 17' () 7' +) ;7' $nswer % ar ;
<) $ =!!-g piece of metal at 1!.!7' is dropped into a cup containing =;! g of water at 1;.!7'. The final temperature of the system is measured to be =!.!7'. "hat is the specific heat of the metal, assuming no heat is echanged with the surroundings or the cup# The specific heat of water is =15! >43kg?9). $) 1=43kg ? 9) %) 6! >43kg ? 9) ') =! >43kg ? 9) () <6! >43kg ? 9) +) =6! >43kg ? 9) $nswer $ ar ;
6) $n 6!-g aluminum calorimeter contains 6! g of water at an equilibrium temperature of $ piece of metal, initially at is added to the calorimeter. The final temperature at equilibrium is 7'. $ssume there is no eternal heat echange. The specific heats of aluminum and water are 51! >4kg?9 and =15! >4kg?9, respecti*ely. The specific heat of the metal is closest to $) ;! >4kg ? 9. %) =6! >4kg ? 9. ') 5! >4kg ? 9. () ;! >4kg ? 9. +) ;! >4kg ? 9. $nswer $ ar ;!D
5) $ copper cylinder with a mass of 1; g and temperature of =;7' is cooled by dropping it into a glass beaker containing ;; g of water initially at !.!7'. The mass of the beaker is ;!.! g and the specific heat of the glass is 6=! >4kg?9. "hat is the final equilibrium temperature of the system, assuming the cooling takes place *ery quickly, so that no energy is lost to the air# The specific heat of copper is 6; >4kg?9 and that of water is =15! >4kg?9. $nswer .=7' ar 1
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1!) "hat is the steady state rate of heat flow through a pane of glass that is =!.! cm by !.! cm with a thickness of =.!! mm when the outside temperature of the glass is -1!.!7' and its inside temperature is ;.!7'# The thermal conducti*ity of glass is !.1!; "43m?9), the specific heat of glass is !.16! cal43g?7'), and 1 cal C =.15! >. $) =. " %) .61 " ') 16. " () =<. " +) 11! " $nswer + ar 1
11) Ender steady state conditions, a piece of wood ;! mm by ;! mm and 1; mm thick conducts heat through its thickness and loses no appreciable heat through its well-insulated sides. The rate of heat flow is measured to be 1=.! " when the temperature difference across its thickness is 6 '7. (etermine the thermal conducti*ity of this wood. $) 5. @ 1!-= "43m?'7) %)
1) $ solid concrete wall =.! m by .= m and ! cm thick, with a thermal conducti*ity of 1. "4 3m?9), separates a basement at 167' from the ground outside at 7'. Ender steady state conditions, how much heat flows through the wall in one hour# $) 1.6 F> %) 1.6 k> ') ;!! > () ;.! F> +) ;.! k> $nswer $ ar 1
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1) Two metal rods, one sil*er and the other copper, are both attached to a steam chamber as shown in the figure, with a temperature of 1!!7', at one end, and an ice water bath, with a temperature of !7', at the other. The rods are ;.! cm long and ha*e a square cross-section, .! cm on a side. "hen steady state has been reached, how much heat flows through the two rods in 1.! min# The thermal conducti*ity of sil*er is =1< "43m?9), and that of copper is 5; "43m?9). No heat is echanged between the rods and the surroundings, ecept at their ends.
$) ! k> %) 5 k> ') =< k> () =5 k> +) 11 k> $nswer % ar 1
1=) $ heat conducting rod, !.5! m long, is made of an aluminum section that is !.1! m long, and a copper section that is
long. %oth sections ha*e cross-sectional areas of
The
aluminum end is maintained at a temperature of and the copper end is at . The thermal conducti*ity of aluminum is !; "4m?9 and of cop per is 6; "4m?9. Gteady state has been reached, and no heat is lost through the well-insulated sides of the rod. The temperature of the aluminum-copper /unction in the rod is closest to $) 17'. %) ;67'. ') ;7'. () ;=7'. +) ;7'. $nswer $ ar ;!D
1;) $ heat conducting rod, 1.=! m long, is made of an aluminum section that is !.;! m long and a copper section that is
long. %oth sections ha*e cross-sectional areas of
The
aluminum end and the copper end are maintained at temperatures of and respecti*ely. The thermal conducti*ity of aluminum is !; "4m?9 of copper is 6; "4m?9. The rate at which heat is conducted in the rod is closest to $) ! ". %) 16 ". ') ". () ; ". +) 6 ". $nswer $ ar ;!D 'opyright 0 !1 2earson +ducation, Inc.
1) Gome properties of glass are listed here. (ensity !! kg4m Gpecific heat 6=! >4kg?'7 'oefficient of linear thermal epansion 6.; @ 1!- 3'7)-1 Thermal conducti*ity !.6! "43m?'7) $ glass window pane is .< m high, .= m wide, and .! mm thick. The temperature at the inner surface of the glass is and at the outer surface =.!7'. Aow much heat is lost each hour through the window under steady state conditions# $) 1.< @ 1!6 > %) 1.< @ 1!; > ') =.< @ 1!= > () =.< @ 1!1 > +) 1.< @ 1! > $nswer $ ar ;!D
1<) $ cylindrical bar that us well insulated around its sides connects hot and cold reser*oirs and conducts heat at a rate of 1!.! >4s under steady state conditions. If all of its linear dimensions 3diameter and length) are reduced by half, the rate at which it will now conduct heat between the same reser*oirs is closest to $) 6!.! >4s. %) !.! >4s. ') ;.!! >4s. () .;! >4s. +) 1.; >4s. $nswer ' ar 1
16) $ concrete wall of a cold storage room measures .! m high, ;.! m wide, and ! cm thick. The room temperature is maintained at -1!7' and the outside temperature is !7' The inside wall is to be co*ered by a layer of wood in order to reduce the rate of heat loss through the wall %H 5! percent. The thermal conducti*ities of concrete and wood are !.6! "4m?9 and !.!=! "4m?9, respecti*ely. Ender steady state conditions, the thickness of the layer of wood required is closest to $) ! mm. %)
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15) The filament in a light bulb has a diameter of !.!;! mm and an emissi*ity of 1.!. The temperature of the filament is !!!7'. "hat should be the length of the filament so it will radiate ! " of power# The Gtefan-%oltmann constant is ;.
!) $ blacksmith is flattening a steel plate that measures 1! cm @ 1; cm @ 1 mm. Ae has heated the plate to 5!! 9. If the emissi*ity of the plate is !.<;, what is the total rate at which it radiates energy# The Gtefan-%oltmann constant is ;.
1) %etelgeuse is a red supergiant star in the constellation Jrion. It radiates heat at the rate of .
) $ cube at 1!!.!7' radiates heat at a rate of 6!.! >4s. If the length of each side is cut in half, the rate at which it will now radiate is closest to $) ;. >4s. %) =!.! >4s. ') 6. >4s. () !.! >4s. +) 1!.! >4s. $nswer ( ar 1
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) $ cube at 1!!7' radiates heat at a rate of 6!.! >4s. If its surface temperature is increased to !!7', the rate at which it will now radiate is closest to $) 1! >4s. %) !< >4s. ') ! >4s. () =! >4s. +) 16! >4s. $nswer % ar 1
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