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.A measurement of interest in the summer is thetemperature-humidity index, consisting of the sum ofthe temperature and the percentage relative humidity.How would you measure this? Sketch a simpleschematic diagram.
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In the summer, humidity interacts with the outdoor temperature, making a person feel hotter due to a reduced heat loss from the skin caused by higher humidity. The temperature-humidity index, Th, is what the temperature would have to be with no humidity in order to give the same heat effect. One index often used is given by Th = 1.98T - 1.09(1 - H)(T - 58) - 56.9, where T is the air temperature, in degrees Fahrenheit, and H is the relative humidity, expressed as a decimal. Find the temperature-humidity index if T = 78° and H = 60%. The temperature-humidity index at 78° and 60% humidity is (Round to one decimal place as needed.)
AT = 2.70 + 0.885 × air temperature − 78.7 × relative humidity + 1.20 × air temperature × relative humidity a. Suppose the air temperature is 90°F. Sketch a graph of the apparent temperature as a function of relative humidity. Describe your graph and what it tells you about humidity levels when the temperature is 90°. b. Suppose the air temperature is 60°F. Sketch a graph of the apparent temperature as a function of relative humidity. Describe your graph and what it tells you about humidity levels when the temperature is 60° and how this compares to your graph and description in part (a) of this Exploration. c. Fill in the following table. Describe how apparent temperature changes when the air temperature increases 15°F from 60 to 75° and from 75 to 90° at 20% relative humidity versus 50% relative humidity versus 90% relative humidity. What is the rate of change of apparent temperature over each of these intervals? Temperature Relative Humidity 0.20 0.50 0.90 60° 75° 90°
Temperature-humidity heat index. In the summer, humidity interacts with the outdoor temperature, making a person feel hotter because of reduced heat loss from the skin caused by higher humidity. The temperature-humidity index, $T_{\mathrm{h}},$ is what the temperature would have to be with no humidity in order to give the same heat effect. One index often used is given by $$T_{\mathrm{h}}=1.98 T-1.09(1-H)(T-58)-56.9$$ where $T$ is the air temperature, in degrees Fahrenheit, and H is the relative humidity, expressed as a decimal. Find the temperature-humidity index in each case. Round to the nearest tenth of a degree. $$T=78^{\circ} \mathrm{F} \text { and } \mathrm{H}=100 \%$$
Functions of Several Variables
Partial Derivatives
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