Hyperthermia of 5°C (i.e., 5°C rise above the normal body temperature) is considered fatal. Express this fatal level of hyperthermia in (a) K, (b) °F, and (c) R.

Understand the Problem

The question is asking to convert a rise in body temperature due to hyperthermia, specifically 5°C, into other temperature scales: Kelvin (K), Fahrenheit (°F), and Rankine (R). This involves understanding the relationships between these different temperature units.

Answer

(a) $5 \, \text{K}$, (b) $9.0 \, \text{°F}$, (c) $9.0 \, \text{R}$

Steps to Solve

Convert Celsius to Kelvin

To convert a temperature change from Celsius (°C) to Kelvin (K), note that the magnitude of change is identical. Thus, a rise of 5°C corresponds directly to:

$$ 5 , \text{°C} = 5 , \text{K} $$

Convert Celsius to Fahrenheit

To convert a change of temperature from Celsius to Fahrenheit, use the conversion formula:

$$ \Delta F = \Delta C \times 1.8 $$

Substituting the temperature change:

$$ \Delta F = 5 \times 1.8 = 9.0 , \text{°F} $$

Convert Celsius to Rankine

To convert a change from Celsius to Rankine, we also use a similar approach as with Fahrenheit:

$$ \Delta R = \Delta C \times 1.8 $$

Substituting the temperature change:

$$ \Delta R = 5 \times 1.8 = 9.0 , \text{R} $$

(a) $5 , \text{K}$

(b) $9.0 , \text{°F}$

More Information

This conversion shows that a rise of 5°C is equivalent to a rise of 5 K, 9.0 °F, and 9.0 R. The unique properties of the Celsius, Kelvin, Fahrenheit, and Rankine scales allow for direct transformations of temperature changes.

Tips

Forgetting the Direct Relationship: A common mistake is misinterpreting the Celsius and Kelvin conversions thinking they don't have the same magnitude.
Incorrectly Applying the Conversion Factors: Ensure that the conversion formulas are correctly used, particularly for Fahrenheit which involves multiplication by 1.8.

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