Question

The temperatures of two bodies differ by 1°C. How much will they differ on Fahrenheit scale?

• A. 1°F
• B. 1.2°F
• C. 2.4°F
• D. 1.8°F

Hint:

To convert a temperature difference from Celsius to Fahrenheit, multiply by 1.8.

Answer 1

The Correct Option is D

Step 1: Pick two reference points.
Take the freezing point of water, 0°C, and a point 1°C above it, 1°C. These are exactly 1°C apart, which is what the question asks about.

Step 2: Convert both points to Fahrenheit.
The conversion rule is \( F = \frac{9}{5}C + 32 \).
At 0°C: \( F_1 = \frac{9}{5}(0) + 32 = 32^{\circ}F \).
At 1°C: \( F_2 = \frac{9}{5}(1) + 32 = 1.8 + 32 = 33.8^{\circ}F \).

Step 3: Find the gap on the Fahrenheit side.
\[ F_2 - F_1 = 33.8 - 32 = 1.8^{\circ}F \]
Notice the plus 32 cancels out completely when we take a difference, so it never matters for gap questions like this one, only the 9/5 factor does.

Step 4: Final Answer.
A 1°C gap always shows up as a 1.8°F gap on the Fahrenheit scale.
\[ \boxed{1.8^{\circ}F} \]

Answer 2

Instead of converting two temperatures, this method starts from the two fixed points that define both scales and works out the ratio directly.

1. 1°F: Would mean the two scales move in lockstep, one degree for one degree. That is not how Celsius and Fahrenheit are built, so this can be ruled out before any calculation.
2. 1.2°F: Water freezes at 0°C and boils at 100°C, a 100 degree span. On the Fahrenheit scale, the same water freezes at 32°F and boils at 212°F, a 180 degree span. Dividing 180 by 100 gives 1.8, not 1.2, so this option does not fit the fixed points.
3. 2.4°F: This is too large a rate. The 180/100 ratio from the fixed points simplifies to 9/5 = 1.8, so any value above 1.8 overstates how fast Fahrenheit changes for each Celsius degree.
4. 1.8°F: The 180 Fahrenheit degrees between freezing and boiling correspond to the same 100 Celsius degrees. So for every 1°C change, the Fahrenheit reading changes by \( \frac{180}{100} = \frac{9}{5} = 1.8 \) degrees.

Since the ratio of the two scales is fixed by their freezing and boiling points at 9/5, any 1°C difference always converts to a 1.8°F difference, no matter which two temperatures are being compared.

The correct answer is 1.8°F.