On a new temperature scale the steam point is 348 °X, and the ice point is 112 °X. What is the temperature on this scale that corresponds to 28.0 °C?
To find the temperature on the new scale that corresponds to 28.0 °C, we need to understand the relationship between the two temperature scales.
Since the steam point is higher than the ice point on the new scale, we can assume that the new scale has a positive linear relationship with the Celsius scale. This means that as the temperature increases on the Celsius scale, it also increases on the new scale.
To determine this relationship, we need to find the temperature difference between the steam point and the ice point on both scales.
On the Celsius scale:
Steam point = 100 °C
Ice point = 0 °C
Temperature difference on the Celsius scale = 100 °C - 0 °C = 100 °C
On the new scale:
Steam point = 348 °X
Ice point = 112 °X
Temperature difference on the new scale = 348 °X - 112 °X = 236 °X
Now that we have both temperature differences, we can find the conversion factor between the two scales.
Conversion factor = Temperature difference on the new scale / Temperature difference on the Celsius scale
Conversion factor = 236 °X / 100 °C = 2.36 °X/°C
To convert 28.0 °C to the new scale, we can multiply it by the conversion factor:
Temperature on the new scale = 28.0 °C * 2.36 °X/°C = 66.08 °X
Therefore, the temperature on the new scale that corresponds to 28.0 °C is approximately 66.08 °X.