Answer: The lowest outside temperature for which the sleeping bag provides adequate protection is approximately 89.61°C below the hiker's skin temperature of 34°C.
Explanation:
To find the lowest outside temperature for which the sleeping bag provides adequate protection, we need to determine the rate of heat loss through conduction and compare it to the heat loss the hiker can safely tolerate.
The rate of heat loss through conduction can be calculated using the formula:
Q = (k * A * ΔT) / d
Where:
Q is the rate of heat transfer (in Watts)
k is the coefficient of thermal conductivity (0.019 Wm¹¹°C-¹ in this case)
A is the surface area (1.3 m² in this case)
ΔT is the temperature difference (in this case, the difference between the skin temperature and the outside temperature)
d is the thickness of the sleeping bag (30 mm, which needs to be converted to meters by dividing by 1000)
Let's plug in the values:
Q = (0.019 * 1.3 * ΔT) / (30 / 1000)
The hiker can safely lose 85 W of heat, so we can set up the equation:
85 = (0.019 * 1.3 * ΔT) / (30 / 1000)
To solve for ΔT, we can rearrange the equation:
ΔT = (85 * (30 / 1000)) / (0.019 * 1.3)
ΔT ≈ 89.61°C