Thermodynamics

Chapter 2 | 777 cents per kWh, determine annual energy cost of lighting for this classroom.Also, discuss the effect of lighting on the heating and air-conditioningrequirements of the room.Solution The lighting of a classroom by fluorescent lamps is considered.The annual electricity cost of lighting for this classroom is to be determined,and the lighting’s effect on the heating and air-conditioning requirementsis to be discussed.Assumptions The effect of voltage fluctuations is negligible so that each fluorescentlamp consumes its rated power.Analysis The electric power consumed by the lamps when all are on andthe number of hours they are kept on per year areLighting power 1Power consumed per lamp2 1No. of lamps2 180 W>lamp2 130 lamps2 2400 W 2.4 kWOperating hours 112 h>day21250 days>year2 3000 h>yearThen the amount and cost of electricity used per year becomeLighting energy 1Lighting power21Operating hours2 12.4 kW2 13000 h>year2 7200 kWh>yearLighting cost 1Lighting energy2 1Unit cost2 17200 kWh>year21$0.07>kWh2 $504>yearLight is absorbed by the surfaces it strikes and is converted to thermal energy.Disregarding the light that escapes through the windows, the entire 2.4 kW ofelectric power consumed by the lamps eventually becomes part of thermalenergy of the classroom. Therefore, the lighting system in this room reducesthe heating requirements by 2.4 kW, but increases the air-conditioning load by2.4 kW.Discussion Note that the annual lighting cost of this classroom alone is over$500. This shows the importance of energy conservation measures. If incandescentlight bulbs were used instead of fluorescent tubes, the lighting costswould be four times as much since incandescent lamps use four times asmuch power for the same amount of light produced.EXAMPLE 2–14Conservation of Energy for an OscillatingSteel BallzThe motion of a steel ball in a hemispherical bowl of radius h shown in Fig.2–51 is to be analyzed. The ball is initially held at the highest location atpoint A, and then it is released. Obtain relations for the conservation ofenergy of the ball for the cases of frictionless and actual motions.hA1SteelballCSolution A steel ball is released in a bowl. Relations for the energy balanceare to be obtained.Assumptions The motion is frictionless, and thus friction between the ball,the bowl, and the air is negligible.Analysis When the ball is released, it accelerates under the influence ofgravity, reaches a maximum velocity (and minimum elevation) at point B at0FIGURE 2–51Schematic for Example 2–14.B2