# Difference between Celsius and Fahrenheit leads to unexpected observations.

Say city A has a temperature of 54 F(12.2 C) and city B has a temperature of 44 F(6.7 C). Their difference is 10 F which is about -12.2 C. I mean what!? This means that 44 F(6.7 C) > 54 F(12.2 C) or 12.2 C - 6.7 C = -12.2C. How is this possible? Is this question silly??

• In the Kelvin scale, A has 285.2K and B has 279.7K. Do you see why their difference is not 261.2K (which would correspond to 10°F) and also not 278.5K (which would correspond to 5.5°C) or 267.5K (which woul dcorrespond to -5.5°C), but simply 5.5K? Jan 25, 2019 at 17:01
• Which one is greater: 1 meter above the floor, or 1 foot above the table? Jan 25, 2019 at 17:19

If two scales have non-coincident zeros, the quantity differences will have transformation law that is different from quantity itself:

$$y =ax+b,\qquad \text{but}\qquad \Delta y = y_2-y_1 = (ax_2+b)-(ax_1+b)=a(x_2-x_1)=a\Delta x$$

For Fahrenheit and Celsius: $$F = 1.8C+32,\qquad \text{but}\qquad\Delta F = 1.8\Delta C$$

so difference in 10°F is 5.55°C.

You're evaluating a difference of temperatures, not a temperature; since there are $$9$$ degrees Fahrenheit to $$5$$ degrees Celsius, the difference in temperature of the two towns, in degrees Celsius, is $$\frac{5}{9}\cdot 10\approx 5.56$$

The temperatures yesterday here were: maximum $$5$$℃, minimum $$-3$$℃. They correspond to $$41$$℉/$$26.6$$℉.

The difference in degrees Celsius is $$8$$, which corresponds to $$\frac{9}{5}\cdot 8=14.4$$ degrees Fahrenheit, and this agrees with the given data. The fact that a temperature of $$14.4$$℉ is about $$-9.78$$℃ is of no concern.