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Dew point temperature, in degrees Celsius (^(@)C), is defined as the temperature to which the air would have to cool in order to reach saturation. For a temperature of 35^(@)C, an estimate of the dew point can be obtained by first subtracting 20^(@)C from the temperature, and then adding 1^(@) for every increase of 5 points in the relative humidity, R. If the dew point is 30^(@)C, which of the following equations best models the situation? Choose 1 answer: 30=15-(1)/(5)R 30=15+5R 30=15-5R 30=15+(1)/(5)R

Dew point temperature, in degrees Celsius (∘C) \left({ }^{\circ} \mathrm{C}\right) , is defined as the temperature to which the air would have to cool in order to reach saturation. For a temperature of 35∘C 35^{\circ} \mathrm{C} , an estimate of the dew point can be obtained by first subtracting 20∘C 20^{\circ} \mathrm{C} from the temperature, and then adding 1∘ 1^{\circ} for every increase of 55 points in the relative humidity, R R . If the dew point is 30∘C 30^{\circ} \mathrm{C} , which of the following equations best models the situation?\newlineChoose 11 answer:\newline(A) 30=15−15R 30=15-\frac{1}{5} R \newline(B) 30=15+5R 30=15+5 R \newline(C) 30=15−5R 30=15-5 R \newline(D) 30=15+15R 30=15+\frac{1}{5} R

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Q. Dew point temperature, in degrees Celsius (∘C) \left({ }^{\circ} \mathrm{C}\right) , is defined as the temperature to which the air would have to cool in order to reach saturation. For a temperature of 35∘C 35^{\circ} \mathrm{C} , an estimate of the dew point can be obtained by first subtracting 20∘C 20^{\circ} \mathrm{C} from the temperature, and then adding 1∘ 1^{\circ} for every increase of 55 points in the relative humidity, R R . If the dew point is 30∘C 30^{\circ} \mathrm{C} , which of the following equations best models the situation?\newlineChoose 11 answer:\newline(A) 30=15−15R 30=15-\frac{1}{5} R \newline(B) 30=15+5R 30=15+5 R \newline(C) 30=15−5R 30=15-5 R \newline(D) 30=15+15R 30=15+\frac{1}{5} R
  1. Start with given temperature: To find the equation that models the dew point temperature, we start with the given temperature of 35 ∘C35\,^\circ\mathrm{C}.
  2. Subtract to get base value: Subtract 20 ∘C20\,^\circ\mathrm{C} from the temperature to get the base value for the dew point estimate.\newline35 ∘C−20 ∘C=15 ∘C35\,^\circ\mathrm{C} - 20\,^\circ\mathrm{C} = 15\,^\circ\mathrm{C}
  3. Add for each increase in humidity: For every increase of 55 points in the relative humidity RR, we add 1∘C1^\circ\text{C} to the base value. This means that for each point of relative humidity, we add (1/5)∘C(1/5)^\circ\text{C}.
  4. Find relationship between variables: The dew point is given as 30∘C30^\circ\text{C}. We need to find the relationship between the dew point, the base value (15∘C15^\circ\text{C}), and the relative humidity RR.
  5. Derive the equation: The equation that represents the situation is:\newlineDew point = Base value + (15)∘C×R(\frac{1}{5})^\circ\text{C} \times R\newline30∘C=15∘C+(15)∘C×R30^\circ\text{C} = 15^\circ\text{C} + (\frac{1}{5})^\circ\text{C} \times R
  6. Match with given options: We need to find which of the given options matches the equation we derived.\newlineThe correct equation is:\newline30=15+15R30 = 15 + \frac{1}{5}R

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