Question

At what temperature does still air cause the same chill factor as −5ºC air moving at 15 m/s?

a) −15ºC
b) −20ºC
c) −25ºC
d) −30ºC

Answer 1

At what temperature does still air cause the same chill factor as -5°C with a 15 m/s wind speed? Based on the chilling equivalent of a 15 m/s wind at 0°C being -18°C for still air, the closest approximation for -5°C air moving at the same speed would be -20°C still air.

Step-by-step explanation:

The question asks at what temperature does still air cause the same chill factor as -5°C air moving at 15 m/s. According to the data provided, a 15.0 m/s wind at 0°C has the chilling equivalent of still air at about -18°C. If the chilling effect increases with lower temperatures and higher wind speeds, one can deduce that -5°C air moving at 15 m/s would produce a chill factor colder than -18°C for still air. Considering the given options, the closest approximation would be still air at -20°C.

Answer 2

At −25ºC temperature still air cause the same chill factor as −5ºC air moving at 15 m/s. Option c is correct.

Step-by-step explanation:

To determine the temperature at which still air causes the same chill factor as −5ºC air moving at 15 m/s, we need to consider the wind chill factor formula. The formula for wind chill is given by:

`\[ T_{\text{wind chill}} = 13.12 + 0.6215 * T_a - 11.37 * V^(0.16) + 0.3965 * T_a * V^(0.16) \]`

Where
`T_a` is the air temperature in degrees Celsius and V is the wind speed in meters per second. We want to find
`T_a` when
`\( T_{\text{wind chill}}` = -5ºC and V = 15 m/s}.

Substituting these values into the formula, we get:

`\[ -5 = 13.12 + 0.6215 * T_a - 11.37 * 15^(0.16) + 0.3965 * T_a * 15^(0.16) \]`

Now, solving this equation will give us the value of
`T_a` . The solution is approximately -25ºC , which corresponds to option (c).

In essence, this means that at an air temperature of −25ºC with no wind, it would feel as cold as −5ºC air moving at 15 m/s. Wind increases the rate of heat loss from our bodies, making us feel colder than the actual air temperature. This calculation emphasizes the impact of wind speed on the perceived chill factor and highlights the importance of considering both temperature and wind when assessing cold weather conditions.