PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HOMEWORK PROBLEMS Chapter 11 ENERGY IN THERMAL PROCESSES HW 11 PART A Hand in your answers in class on scantron on Monday 29 November 2010 Write your name class 1401 and HW 11 on the scantron 1 Convert 3 50 x 103 cal to an equivalent number of joules a 2 74 X 104 J b 1 47 X 104 J c 3 24 X 104 J d 5 33 X 104 J From the mechanical equivalent of heat 1 cal 4 186 J Therefore 4 186 J 3 50 103 cal 3 50 103 cal 1 47 10 4 J 1 cal 2 Convert 7 80 x 105 J to the equivalent number of Calories 1 Cal 1 000 cal a 186 Cal b 238 Cal c 325 Cal d 418 Cal e 522 Cal 1 cal 1 Cal 7 80 10 5 J 7 80 105 J 186 Cal so a is the correct choice note cal vs Cal 103 cal 4 186 J 3 How much energy is required to raise the temperature of 5 00 kg of lead from 20 0 C to its melting point of 327 C a 4 04 X 105 J b 1 07 X 105 J c 8 15 X 104 J d 2 13 X 104 J e 1 96 X 105 J The required energy input is Q mc DT 5 00 kg 128 J kg C 327 C 20 0 C 1 96 10 5 J and the correct response is e 4 If 9 30 X 105 J of energy are transferred to 2 00 kg of ice at 0 C what is the final temperature of the system a 22 4 C b 14 2 C c 31 5 C d 18 0 C e 0 C The energy which must be added to the 0 C ice to melt it leaving liquid at 0 C is Q1 mL f 2 00 kg 3 33 10 5 J kg 6 66 10 5 J 5 5 5 Once this is done there is Q2 Qtotal Q1 9 30 10 J 6 66 10 J 2 64 10 J of energy still available to raise the temperature of the liquid The change in temperature this produces is Q2 2 64 105 J DT T f 0 C 31 5 C mcwater 2 00 kg 4 186 J kg C C 31 5 C 31 5 C and the correct choice is c so the final temperature is T f 0 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 11 5 A wall made of wood 4 00 cm thick has area of 48 0 m2 If the temperature inside is 25 C and the temperature outside is 14 C at what rate is thermal energy transported through the wall by conduction a 82 W b 210 W c 690 W d 1 3 X 103 W e 2 1 X 103 W The rate of energy transfer by conduction through a wall of area A and thickness L is P kA Th Tc L where k is the thermal conductivity of the material making up the wall while Th and Tc are the temperatures on the hotter and cooler sides of the wall respectively For the case given the transfer rate will be 25 C 14 C 1 3 10 3 J s 1 3 10 3 W J P 0 10 48 0 m 2 s m C 4 00 10 2 m and the d is the correct answer 6 A granite ball of radius 2 00 m and emissivity 0 450 is heated to 135 C whereas the ambient temperature is 25 0 C What is the net power radiated from the ball a 425 W b 3 55 X 104 W c 145 W d 2 01 X 103 W e 2 54 X 104 W The power radiated by an object with emissivity e surface area A and absolute temperature T 4 4 in a location with absolute ambient temperature T0 is given by P s Ae T T0 8 2 4 where s 5 669 6 10 W m K is a constant Thus for the given spherical object A 4pr 2 we have P 5 669 6 10 8 W m 2 K 4 4p 2 00 m 2 0 450 408 K 4 298 K 4 yielding P 2 54 10 4 W so e is the correct choice 7 How long would it take a 1 00 X 103 W heating element to melt 2 00 kg of ice at 20 0 C assuming all the energy is absorbed by the ice a 4 19 s b 419 s c 555 min d 12 5 min e 2 00 h C before it will start to The temperature of the ice must be raised to the melting point DT 20 0 melt The total energy input required to melt the 2 00 kg of ice is 5 Q mcice DT mL f 2 00 kg 2 090 J kg C 20 0 C 3 33 105 J kg 7 50 10 J The time the heating element will need to supply this quantity of energy is Q 7 50 105 J 1 min Dt 750 s 12 5 min 3 60 s P 1 00 10 J s making d the correct choice 8 An unknown element of mass 0 250 kg initially at 95 0 C is dropped into 0 400 kg of water at 20 0 C contained in an insulated cup of negligible mass and specific heat If the equilibrium temperature is 36 0 C which of the following is the most likely identity of the substance a aluminum b beryllium c cadmium d iron e gold We use Qhot Qcold or m x cx T f Tx i mw cw T f Tw i 2 to compute the specific heat of the PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 11 unknown material and find cx T mw cw T f Tw i mx f Tx i 0 400 kg 4 186 J kg C 36 0 C 0 250 kg 36 0 C 95 0 C 20 0 C 1 82 103 J kg C which is a match for the specific heat of Beryllium so b is the correct choice 9 An amount of energy is added to ice raising its temperature from 10 C to 5 C A larger amount of energy is added to the same mass of water raising its temperature from 15 C to 20 C From these results what can we conclude a Overcoming the latent heat of fusion of ice requires an input of energy b The latent heat of fusion of ice delivers some energy to the system c The specific heat of ice is less than that of water d The specific heat of ice is greater than that of water e More information is needed to draw any conclusion Since less energy was required to produce a 5 C …