Answer
We can use this formula to convert from $^{\circ}J$ to $^{\circ}C$:
$C = \frac{192}{144}J - 114$
Work Step by Step
The temperature range from the freezing point to the boiling point is $0^{\circ}J$ to $144^{\circ}J$, which corresponds with $-114^{\circ}C$ to $78^{\circ}C$.
The temperature change from the freezing point to the boiling point is $+144^{\circ}J$ which is $+192^{\circ}C$
To convert from $^{\circ}J$ to $^{\circ}C$, we need to multiply by a factor of $\frac{192}{144}$.
Since $0^{\circ}J$ corresponds with $-114^{\circ}C$, we also need to subtract a value of $114$
We can use this formula to convert from $^{\circ}J$ to $^{\circ}C$:
$C = \frac{192}{144}J - 114$
We can check this formula with the freezing point and boiling point:
$C = \frac{192}{144}(0) - 114 = -114^{\circ}C$
$C = \frac{192}{144}(144) - 114 = 78^{\circ}C$
