Enter the temperature range at which you found your sugar melted.
Your measurement suggests that your oven has the approximate calibration curve
T = Tdial + 367 - Tmelt (if you use degrees Fahrenheit)
T = Tdial + 186 - Tmelt (if you use degrees Celsius)
where Tdial is the temperature of the dial. Note that if your dial says that sugar melts at 400˚F, this formula states that the actual temperature in the oven is the temperature that the sugar melts (366˚F).
The range that I found that the sugar melted in my oven was around 350 to 360. however, what exactly does the Tdial aspect of the problem mean, it just confused me a bit.
as they stated quite clearly,
Tdial is the temperature of the dial
that is, the temperature you set, as opposed to the actual temperature. No dial is entirely accurate.
So my Tdial would be 360 right? Since that is where I had my dial set to and the sugar melted around that temperature.
In the given problem, Tdial represents the temperature displayed on the dial of your oven. It is the value you set or select on the oven's temperature control. The equation T = Tdial + 367 - Tmelt (in Fahrenheit) or T = Tdial + 186 - Tmelt (in Celsius) relates the temperature that the sugar melts (Tmelt) to the actual temperature inside the oven (T).
To find the temperature range at which the sugar melted in your oven (around 350 to 360), we need to work backwards using the given equation. Let's say the dial temperature for your oven is X (Tdial = X).
For Fahrenheit: T = X + 367 - Tmelt
350 = X + 367 - Tmelt (lower end of the range)
360 = X + 367 - Tmelt (upper end of the range)
For Celsius: T = X + 186 - Tmelt
350 = X + 186 - Tmelt (lower end of the range)
360 = X + 186 - Tmelt (upper end of the range)
By rearranging these equations, we can solve for Tmelt:
For Fahrenheit:
Tmelt = X + 367 - 350 = X + 17 (lower end of the range)
Tmelt = X + 367 - 360 = X + 7 (upper end of the range)
For Celsius:
Tmelt = X + 186 - 350 = X - 164 (lower end of the range)
Tmelt = X + 186 - 360 = X - 174 (upper end of the range)
So, the temperature range at which you found the sugar melted in your oven is approximately X + 17 to X + 7 degrees Fahrenheit (if using Fahrenheit) or X - 164 to X - 174 degrees Celsius (if using Celsius), where X represents the dial temperature of your oven.