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What is the temperature 37.6 °C expressed in degrees Fahrenheit?
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1. Intro to General Chemistry
Temperature
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Which equation correctly converts a temperature from degrees Celsius (c) to degrees Fahrenheit (f)?
A
f = (9/5) c + 32
B
f = (c + 32) / (9/5)
C
f = (9/5) c - 32
D
f = (5/9) c + 32
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Recall the relationship between Celsius and Fahrenheit temperature scales, which is based on the freezing and boiling points of water.
Understand that the formula to convert Celsius (c) to Fahrenheit (f) involves scaling the Celsius temperature by a factor and then adding an offset to align the freezing points.
The general form of the conversion is: \(f = m \times c + b\), where \(m\) is the scaling factor and \(b\) is the offset.
Since water freezes at 0°C and 32°F, and boils at 100°C and 212°F, calculate the scaling factor \(m\) as the ratio of the Fahrenheit temperature change to the Celsius temperature change: \(m = \frac{212 - 32}{100 - 0} = \frac{180}{100} = \frac{9}{5}\).
The offset \(b\) corresponds to the Fahrenheit temperature when Celsius is zero, which is 32, so the full conversion formula is \(f = \frac{9}{5} c + 32\).
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