Chapter 5 problems Section 5.1 5.1. (I) (a) Normal body temperature is 37°C. Convert this to Fahrenheit.(b) What is the temperature in degrees Celsius of a person with a fever of 104°F? 5.2. (I) (a) Room temperatures are kept at 68°F in the winter to conserve energy. What is this in degrees Celsius? (b) On a summer day the air conditioner is set to come on when the temperature rises above 27°C. How hot is this in degrees Fahrenheit? 5.3. (I) What Fahrenheit temperature corresponds to absolute zero? 5.4. (I) One of the properties that makes tungsten a good material for light bulb filaments is its high melting point of 3410°C. What temperature is this on the Fahrenheit scale? 5.5. (I) Frozen alcohol makes as good a candle as wax, with one significant disadvantage:· Alcohol melts at -114°C. What Fahrenheit temperature is this? 5.6. (I) The temperature of the surface of the sun is about 8000°F. What is this temperature on the Celsius and Kelvin scales? 5.7. (II) At what temperature do the Fahrenheit and Celsius scales have the same numerical value? 5.8. (I) A gap must be left between steel railroad rails to allow for thermal expansion. How large a gap is needed if the maximum temperature reached is 50°C more than the temperature at which the rails were laid? The length of a rail is 10 m. Refer to table 5.1 for the coefficient of linear expansion of steal. 5.9 (I) The Golden Gate Bridge has an overall length of approximately 2800 m. If the bridge experiences temperature extremes from -20° to +40°C, what will its change in length be? The bridge is made primarily of steel. Refer to table 5.1 for the coefficient of linear expansion of steal. how much water will overflow the bottle if the temperature increases to 30°C? You may assume that the bottle is a cube 10 cm on a side. and he is found to be 1. If the original measurement was made at a temperature of 18°C.5. 5. (b) What is the power input in megawatts for this purpose? .14.11.3 we know calories that the specific heat capacity of a human is 0.83 . Sections 5.3 5.10.16. (III) If you have a one liter glass bottle full of water at 20°C. but that of the measuring device does. Calculate the amount of heat in calories that must be removed from a 30-g steel scalpel to reduce its temperature from 150° to 20°C. assuming the heat of fusion is the same as that of water? 5. (I) When a scalpel is sterilized. (II) A man's height is measured by his standing next to a device made of aluminum.13. assuming this is done at 100°C.2 and 5. (I) How many calories of heat would be required to raise the temperature of a 45-kg person by 2. 5. (a) Calculate the amount of heat needed each second just to vaporize the water.15.30-kg package of frozen vegetables originally at 0°C. its temperature may rise to 150°C. How high is it in the summer when its temperature is 20°C? (Because of its size the pyramid warms and cools slowly and does not reach the temperature extremes of the area. (I) How many calories of heat are needed to thaw out a 0. 5. what height would be measured for the same man on a day when the temperature is 35°C? Is this difference enough to be of any concern? Note that the man's temperature doesn't change.80 m tall.0°C? How many food calories is this? From table 5. gi˚C 5. (I) The Great Pyramid of Cheops is 145 m high on a cold winter day when its temperature is 5°C. (I) A large power plant converts 1000 kg of water to steam every second to run its generators.) You may assume that the coefficient of expansion is the same as that for concrete.12. To verify this.0 kg of water to make ice once the water has reached 0°C? (b) How long will it be before all 4.000liter swimming pool. (I) A burn produced by live steam at 100°C is more severe than one produced by the same amount of water at 100°C.17. how long will this take? 5. (b) calculate the heat that must be removed from 5.50 kg of the water? (b) If heat is supplied to the pot of water at the rate of 125 cal/sec.23. (a) calculate the heat that must be removed from 5. 5.0 g of steam at 100°C to condense it and then lower its temperature to 34°C.22.50-kg block of material is heated from 20° to 35°C by the addition of 420 cal of heat.0 kg of water from 25°C to the boiling point and then to boil away 0.0 kg of shaved ice is needed to keep medication cold in a room that has no refrigerator. (II) If a 30-g lead bullet with a speed of 600 m/sec strikes a practice target and half of the thermal energy generated is absorbed by the bullet.0 kg of ice melts if heat enters it at the rate of 25 cal/sec? 5. (II) A 0. 5.20.21. (a) What amount of heat must be removed from 4. (a) What temperature rise occurs if no other heat enters or leaves the pool? (b) How many liters of water would have to evaporate from the pool to keep its temperature constant? 5. what is the temperature increase of the bullet? . and compare this with the answer to part (a).19 (II) On a summer day sunlight may put 100 million calories into an 80. (a) What is the rate of heat loss in watts? (b) How long will it take for this person's temperature to return to 37°C if his mass is 90 kg? 5. (II) (a) How much heat is needed to raise the temperature of a 1. Calculate the specific heat of the block and identify the substance of which it is composed.0 g of water at 100°C to lower its temperature to 34°C (skin temperature).0-kg steel pot containing 2. assuming that it is made of a pure substance. (II) Following strenuous exercise a person has a temperature of 40°C and is giving off heat at the rate of 50 cal/sec.5. (II) Suppose that 4.18. 24. 5.29.0 g of water condenses on a 100-g glass containing 300 g of water at 5. If 8.30 (I) What is the relative humidity on a day when the temperature is 25°C and the air contains 20.30 . (III) An ice cube having a mass of 50 g and an initial temperature of . calculate the temperature increase of her hands given the following information: The force exerted in each of the 20 rubs is 40 N. (III) Warming cold hands by rubbing them together is a time-honored art. the distance moved in each rub is 0.75 kg of soup at 20°C is put into a freezer.20-kg aluminum bowl containing 0. 5.26. and the total mass of the hands is 1.5 concerning the saturation density of water. (III) A 0. what is the final temperature? Assume that the soup has the same thermal properties as water.000 cal from the bowl of soup.0 g/m3 of water vapor? See table 5. . what is giC the temperature increase of the affected material? Assume that friction other than that of the brakes is negligible.27. what will be the final temperature? Ignore the effect of the surroundings.075 m.5. 5.20°C is placed in 400 g of 30°C water.28. What is the final temperature if the effect of the surroundings can be neglected? 5. What is the final temperature of the mixture if the effects of the container can be neglected? 5.25. (II) A 1000-kg car rolls down a hill starting from rest and loses 100 meters in altitude before braking to a stop.5 kg. O°C. 5. If half the thermal energy generated in the brakes calories is absorbed by 20 kg of material having a specific heat of 0. (III) The formation of condensation on a cold glass of water will cause it to warm up faster than it would have otherwise. If a woman rubs her hands back and forth for a total of 20 rubs. (III) Five grams of 20°C water is poured onto a 600-g block of ice that has an initial temperature of -15°C. If the freezer removes 80. 5.4 5.5 m2. Note that this is not much different than for a human in a warm room. as seen in Example 5. (I) What is the density of water vapor in grams per cubic meter in the desert when relative humidity is 10% and air temperature is 40°C? 5. while the outside temperature is 5°C.31. The surface area of the animal is 1. (III) One day the relative humidity is 90% and the temperature is 25°C. 5.36 (I) Calculate the rate of heat conduction in watts out of an animal with 3.8. Note that this is only conduction through the walls and does not include conduction through the windows or ceiling.32.33.34. Heat losses due to convection and conduction can be neglected. .0cm thick fur. (II) The relative humidity is 40% late in the day when the air temperature is 20°C. (III) What is the dew point on a day when the relative humidity is 39% and the temperature is 20°C? 5. 5. 5. its skin tempera e is 35°C. (II) If the relative humidity is 75% on a summer morning when the air temperature is 20°C. and the temperature of the surrounding air is 0°C.37. What will it be later that night when the temperature drops to 10°C? You may assume that the vapor content of the air is constant.35.0 cm thick and have twice the thermal conductivity as glass wool. and the thermal conductivity of the fur can be assumed to be the same as that for air. (a) How many grams of water will condense out of each cubic meter of air if the temperature drops to 15°C? (b) How much energy does the condensation from each cubic meter release? Section 5. what will it be later in the day when the temperature reaches 30°C? Assume that the water-vapor content of the air is constant. (I) Calculate the rate of heat conduction through the walls of a house if they are 8. The total area of the walls is 120 m2 and the inside temperature is 20°C. (II) Compare the rate of heat conduction through an 8. what will the final temperature of the coffee be? Assume the styrofoam cup is such a good insulator that all other forms of heat transfer can be ignored. Note that the "steam" above the coffee is really condensed water vapor droplets. 5.0 g of water evaporate from 150 g of 90°C coffee.0 m2.80 cm if the temperatures at the outer and inner surfaces are 5.43.75-cm-thick window of area 2. calculate it for a window of area 3. an emissivity of 0. 5.98. . 5.41 (I) Glowing embers in a fireplace have a temperature of 850°C.38.39. 5. 5.42. If the temperature of the surroundings is 23°C and 50% of the radiation from the fire enters the room. and a surface area of 0.44. what is the rate of heat transfer into the room in kilowatts? 5.15 m2.Section 5. To see just how large the rate of heat conduction through a glass window is.0-cm-thick wall of area 10 m2 with that through a 0. how much heat is required to melt the iceberg? Note that this amount of energy was released earlier at the origin of the iceberg.2.95.40. (I) What is the rate of heat loss by radiation from a man completely clothed in white (head to foot) if his skin temperature is 34°C and the surrounding temperature is 10°C? His surface area is 1. (II) It is usually cold next to a window on a winter day because heat conduction through the window is rapid enough to cool the air next to it. The thermal conductivity of the wall can be assumed to be twice that of glass wool. (II) If 5. (I) If a small iceberg with a mass of 20 million kg moves south from the Arctic. for the same temperature difference across each.0° and l0˚C respectively.4 continued 5.4 m2 and the emissivity of the clothing is 0. (I) What is the rate of heat loss by radiation from a black roof of area 250 m2 if its temperature is 20°C and that of the surroundings is l0˚C? The emissivity of the roof is 0.0 m2 and thickness 0. 0 m2 if each pane of glass is 1. and the coffee in the pot has a temperature of l00°C. Hint: Calculate the temperature difference across each layer separately and add them together. (III) What is the temperature difference across a double-paned window of area 3.Section 5. If 20 m3 of O°C air enters a room.51. and the rate of heat conduction is 200 W. If the bottom is 0. 5. The specific heat capacity of a human is listed in table 5.49.3 as calories 0.5 5. 5. Use use the value of 580 cal/g. how much heat is required to warm it to 20°C? Section 5.47. gi˚C 5. (I) How many calories of heat would have to be put into the shoulder of a person receiving a heat treatment to raise the shoulder's temperature by 5°C? The mass of the shoulder region is 5. how hot must the underside be to conduct heat into the pot at the rate of 500 W? (b) How many grams of water boil away each second if convection plus boiling is the only method of energy transfer out of the pot? 5. as is the air gap between them.45.000 cal of heat. 0 cm thick. 5. (a) How many calories of heat are . You may assume that convection in the air gap is negligible.4 continued 5. (II) On a day when a man shows no visible perspiration he will still evaporate about 600 g of water from his lungs. and the effect of circulation and other factors can be neglected.83 .0 kg.50. (III) (a) A glass coffee pot has a bottom with an area of 400 cm2.75 cm thick.48 (I) How many calories of heat will a person lose by evaporating 1250 g of water and perspiration in a day? Use use the value of 580 cal/g. (1) Calculate how many grams of perspiration a person must evaporate during physical exercise to get rid of 100. (III) Considerable temperature decreases can occur when cold air blows through an open door.46. assuming all other forms of heat transfer are negligible and that the ice water stays at 0°C? 5. calculate the temperature rise of her body in one hour assuming no heat escapes the suit. 40 min.56. (II) One problem for astronauts is getting rid of waste body heat.57. 5°C? 5. It takes 20 min to bring his temperature down and the surgery lasts 2 hr. If an astronaut is in a spacesuit in the vacuum of space and is awake but relaxed.removed by this evaporation? (b) What is the rate of heat loss in watts due to this process? Section 5. How many kilograms of ice must melt to do this. and comment on the sensitivity needed in a thermograph to observe variations in temperature of 1. and the suit's specific heat is the same as her body's. Skin temperature will rise during exercise.52. how many grams of water and perspiration must he evaporate in order to get rid of half of the waste thermal energy.0°C.5 continued 5. The total mass of the astronaut and suit is 100 kg. (III) An 80-kg patient is to be cooled to 29°C for surgery by being placed in ice water. 5.0 liters of blood are pumped to the surface of a person per minute to carry away core heat. (II) An average man may consume 3000 kcal per day. 05 g/cm3. (III) During heavy exercise 2.54. 5. If the blood is cooled by 2. what is the rate of heat transfer in watts due to blood flow (forced convection)? You may assume that the specific heat of blood is the same as that for water and that the density of blood is 1. and the blood must have a . the blood will not be cooled by that much.97. If he uses all these calories to perform work and produce heat (no storage of fat).0% 5. The power output of this patient is 60 W.0°C at the surface. Note that although the core and skin normally differ in temperature by 3°to 4°C.53.55. (II) (a) Calculate the rate of heat loss by radiation from 10 cm2 of skin if the skin temperature is 33°C and its emissivity is 0. (b) Compare this with the rate of heat loss if the skin temperature were 34°C. (II) How many grams of perspiration must a 50-kg woman evaporate to reduce her temperature by 1. assuming his average efficiency is 5. His body temperature is 2. (III) Suppose a man is losing heat to the environment at the rate of 300 W. If his mass is 76 kg.greater temperature than the skin in order to transfer heat to it through vessel walls (conduction).5 continued 5.58.0°C below normal. how long will it take for his temperature to rise to normal? . Section 5. and he begins to shiver.