Space invaders land on Earth. On the invaders' temperature scale, the ice point is at 33oI (I=invader temp), and the steam point is at 293oI. The invaders' thermometer shows the air temperature on Earth to be 115.68oI. What would this temperature be on the Celsius scale? (no units are necessary for this question--oC is implied)
To convert the temperature from the invaders' scale (oI) to Celsius (oC), we need to establish a conversion formula.
First, we need to find the difference between the steam point and the ice point on the invaders' temperature scale. This would be 293oI - 33oI = 260oI.
Next, we need to find the difference between the steam point and the given temperature of 115.68oI on the invaders' scale. This would be 293oI - 115.68oI = 177.32oI.
Now, we have the two temperature differences, one in the invaders' scale (260oI) and the other in Celsius (oC) (177.32oI). We can set up a proportion based on these differences:
260oI corresponds to a temperature of 100oC
177.32oI corresponds to a temperature of x oC
Using the proportion, we can solve for x:
260oI / 100oC = 177.32oI / x
Cross-multiplying, we get:
260oI * x = 100oC * 177.32oI
Simplifying,
260x = 17732oC
Dividing both sides by 260, we find:
x = 17732oC / 260
x ≈ 68.2oC
Therefore, the air temperature on Earth would be approximately 68.2oC on the Celsius scale.