Hyperthermia of 5°C 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 temperature increase of 5°C into three different temperature scales: Kelvin (K), Fahrenheit (°F), and Rankine (R). This involves applying the appropriate conversion formulas for each scale to express the same amount of hyperthermia.
Answer
- (a) $278.15 \, K$, (b) $41 \, °F$, (c) $499.47 \, R$
Answer for screen readers
- (a) $278.15 , K$
- (b) $41 , °F$
- (c) $499.47 , R$
Steps to Solve
- Convert °C to Kelvin (K)
To convert Celsius to Kelvin, use the formula:
$$ K = °C + 273.15 $$
For a temperature increase of 5 °C:
$$ K = 5 + 273.15 = 278.15 , K $$
- Convert °C to Fahrenheit (°F)
To convert Celsius to Fahrenheit, use the formula:
$$ °F = (°C \times \frac{9}{5}) + 32 $$
For a temperature increase of 5 °C:
$$ °F = (5 \times \frac{9}{5}) + 32 = 9 + 32 = 41 , °F $$
- Convert °C to Rankine (R)
To convert Celsius to Rankine, use the formula:
$$ R = (°C + 273.15) \times \frac{9}{5} $$
For a temperature increase of 5 °C:
$$ R = (5 + 273.15) \times \frac{9}{5} = 278.15 \times \frac{9}{5} = 499.47 , R $$
- (a) $278.15 , K$
- (b) $41 , °F$
- (c) $499.47 , R$
More Information
This temperature increase of 5 °C translates to 278.15 Kelvin, 41 Fahrenheit, and 499.47 Rankine. Understanding these conversions is crucial in fields involving temperature measurement, such as science and engineering.
Tips
- Confusing the formulas for converting between scales.
- Forgetting to add or subtract the correct constants during conversions.
- Not understanding that a temperature change (like a 5 °C increase) is the same in Kelvin since the size of the degree units is the same.
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