Question

The following table gives the heat index (Heat Stress Index) as a function of the air temperature (Environ- mental Temperature) and the Relative Humidity. The heat index is measured in °F, the air temperature is measured in °F, and the relative humidity is measured in %. For this problem we will use the variables I (heat index), T (air temperature), and H (relative humidity). The table presents IT, H). Table 3: Apparent temperature, Heat Stress Index (HSI* Environmental Temperature °F Relative Humidity 70 75 80 85 90 95 100 105 110 115 % 0% 10% 75 20% 82 40% 50% 60% 70% 70 80% 90% 100% Category Extreme danger Danger Extreme caution Caution 73 78 83 87 91 95 99 103 80 85 90 95 100 105 111 72 77 82 87 93 99 105 112 120 73 78 84 90 96 104 113 123 135 74 79 86 93 101 110 123 137 151 75 81 88 96 107 120 135 150 100 114 132 149 77 85 93 106 124 144 86 97 113 136 Extreme Danger 79 88 102 122 80 91 108 Apparent temperature (°F) Dangers Greater than 120 Heat stroke imminent 105-120 Heat exhaustion likely 90-105 Heat cramps, exhaustion possible 80-90 Exercise more fatiguing than normal 72 a. Estimate a value for IT(90,40) and interpret your answer. b. Estimate a value for Iu (90,40) and interpret your answer. c. Give a general description of the contour curve given by ICT, H) = 100, that is explain how the idea of this contour curve makes sense in this problem. Note: Ir =

Answer 1

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lin' F) Solution: Giren, the heat index, It is a function of the - Humidity H.(0%) " Aw temperature, I, and relative T (n °F) .:. [= 111, ). t. 17 (90140) = 25 (90,40) 1 (95,40) - 1(85,40) 95-85 = 101 - 86. 1. = 11.5] Ans. = 101 - 86 15 Interpretation: Keeping the relative humidity fixed at 40% With every additional of change in the air 1. temperature at 90f the heat index increases by 1.5 of (per of of air temps Are 109. It (90,40) = 21 (90,40). 1(90,50) - [(90,30) °F/% 50-30 = 9690 f/n = 10:3) • F/2Ans. 20 Interpretation: Keeping the air temp-fined at 90f, With every additional change in the relative humidity by% at 40% , the heat index increases by 0.3°F (pe % of R. H.) Ana ves. I(TH) = 400. T: 90f, H=60%. the. The heat index is 100°F when the air temp. is 90°F C and relative humidity is 60% under such a situation?" EXTREME CAUTION" is to be taken consta