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Savage Lindsey
02/07/2024 · Middle School

3. On windy days, we will feel cooler compared to calm days without wind. The rate of heat loss, \( H \) (in kilocalories per square meter per hour), when the air temperature, \( t \) (in degrees Celsius), and the wind speed, \( w \) (in meters per second), are determined by the equation \( H=(10.45+10 \sqrt{w}-w)(33-t) \). Evaluate \( H \) when \( t=0 \) and \( w=4 \). a. Evaluate \( \frac{\partial H}{\partial t}, \frac{\partial H}{\partial w} \) when \( t=0 \) and \( w=4 \). Interpret the results! c. When \( t=0 \) and \( w=4 \), Which one has a greater influence on \( H \). a change in wind speed of \( 1 \mathrm{~m} / \mathrm{s} \) or a change in temperature of \( 1{ }^{\circ} \mathrm{Cl} \) ?

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At \( t = 0 \) and \( w = 4 \), the partial derivatives are: - \( \frac{\partial H}{\partial t} = -26.45 \, \text{kcal/m²/hr per} \, ^\circ\text{C} \) - \( \frac{\partial H}{\partial w} = 49.5 \, \text{kcal/m²/hr per m/s} \) A change in wind speed of 1 m/s has a greater influence on heat loss than a change in temperature of 1°C.

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