An iron sphere with a mass of 7.50 g was placed in a boiling water bath and allowed to sit until thermal equilibrium is achieved. Eventually, the hot iron sphere was immersed into a room temperature (about 22 degrees Celsius) water with a mass of 25.0 g. Calculate the final temperature of the water/iron system. The heat capacities of water and iron are 4.18 J/gK and 0.452 J/gK.
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- To help prevent frost damage, 4.00 kg of water at 0 is sprayed onto a fruit tree. (a) How much heat transfer occurs as the water freezes? (b) How much would the temperature of the 200-kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be 3.35k J/kg. , and assume that no phase change occurs in the tree.Repeat the preceding problem, assuming the water is in a glass beaker with a mass of 0.200 kg, which in tum is in a calorimeter. The beaker is initially at the same temperature as the water. Before doing the problem, should the answer be higher or lower than the preceding answer? Comparing the mass and specific heat of the beaker to those of the water, do you think the beaker will make much difference?One of a dilute diatomic gas occupying a volume of 10.00 L expands against a constant pressure of 2.000 atm when it is slowly heated. If the temperature of the gas rises by 10.00 K and 400.0 J of heat are added in the process, what is its final volume?
- At a foundry, 22 kg of molten aluminum witha temperature of 660.4◦C is poured into amold.If this is carried out in a room containing150 kg of air at 25◦C, what is the temperatureof the air after the aluminum is completelysolidified? Assume that the specific heat capacity of air is 1.0×10^3J/kg ·◦C. The specificheat of aluminum is 899 J/kg ·◦ C and its latent heat of fusion is 3.97 × 10^5J/kg.Answer in units of ◦CSolar radiation is incident on a 5 m2 solar absorberplate surface at a rate of 800 W/m2. Ninety-three percent ofthe solar radiation is absorbed by the absorber plate, whilethe remaining 7 percent is reflected away. The solar absorberplate has a surface temperature of 40°C with an emissivityof 0.9 that experiences radiation exchange with the surroundingtemperature of -5°C. In addition, convective heat transferoccurs between the absorber plate surface and the ambientair of 20°C with a convection heat transfer coefficient of7 W/m2∙K. Determine the efficiency of the solar absorber,which is defined as the ratio of the usable heat collected bythe absorber to the incident solar radiation on the absorber.A 200.0 g metal container, insulated on the outside, holds 100.0 g of water in thermalequilibrium at 22.0 oC. A 21.0 g ice cube, at the melting point, is dropped into the water. Whenthermal equilibrium is reached, the temperature is 15.0 °C. Assuming there is no heat exchangewith the surroundings, calculate the specific heat for the metal.[Given cwater = 4186.0 J/kg*K and Lf = 3.34 *10^5 J/kg]
- A 50-m-long section of a steam pipe whose outer diameteris 10 cm passes through an open space at 15°C. The averagetemperature of the outer surface of the pipe is measured to be150°C. If the combined heat transfer coefficient on the outer surfaceof the pipe is 20 W/m2·K, determine (a) the rate of heat lossfrom the steam pipe; (b) the annual cost of this energy lost if steamis generated in a natural gas furnace that has an efficiency of 75percent and the price of natural gas is $0.52/therm (1 therm =105,500 kJ); and (c) the thickness of fiberglass insulation(k = 0.035 W/m·K) needed in order to save 90 percent of the heatlost. Assume the pipe temperature to remain constant at 150°C.In a production facility, 1.2-in-thick, 2-ft *2-ft square brass plates (r = 532.5 lbm/ft3 and cp =0.091 Btu/lbmF) that are initially at a uniform temperatureof 75F are heated by passing them through an ovenat 1300F at a rate of 450 per minute. If the plates remain in the oven until their average temperature rises to 1000F,determine (a) the rate of heat transfer to the plates in thefurnace and (b) the rate of entropy generation associatedwith this heat transfer process.On a cold winter day when the temperature is -20.0 ∘C, what is the amount of heat needed to warm to internal body temperature (37.0∘C) the 0.550 L of air exchanged with each breath? Assume that the specific heat capacity of air is 1020 J/(kg⋅K) and that 1.0 L of air has a mass of 1.3 g. Express your answer in joules. How much heat is lost per hour if the respiration rate is 19.0 breaths per minute?
- The convection heat transfer coefficient for a clothedperson standing in moving air is expressed as h = 14.8V 0.69for 0.15 < V < 1.5 m/s, where V is the air velocity. For aperson with a body surface area of 1.7 m2 and an averagesurface temperature of 29°C, determine the rate of heat lossfrom the person in windy air at 10°C by convection for airvelocities of (a) 0.5 m/s, (b) 1.0 m/s, and (c) 1.5 m/s.In the laboratory, calorimetry can be used to determine the latent heat of fusion of water, LfLf. If an ice cube of mass 30.0g30.0g at 0∘C0∘C is added to a calorimeter cup of mass mc=60.0gmc=60.0g that contains water of mass 170g170g at an initial temperature TiwTiw of 20∘C20∘C, after the ice melts, the final temperature of the water TfwTfw is found to be 5.57∘C5.57∘C. Based on this data, what is the latent heat of fusion of water? The specific heat capacities of water and the calorimeter are 4186J/(kg.K)4186J/(kg.K) and 900J/(kg.K)900J/(kg.K), respectivelyHow much heat transfer (in kilocalories) is required to thaw a 0.450-kg package of frozen vegetables originally at 0C if their heat of fusion is the same as that of water?