I'm working on a question for class where we need to solve for the heat flux in a system. The problem is stated ad follows:
A $2 \; \mathrm{mm}$ thick glass sheet is being used for a window. The thermal conductivity of glass is $1.7 \; \mathrm{J/(m \cdot K \cdot s)}$. The temperature outside is $-20 \; \mathrm{^\circ C}$ and that inside is $20 \; \mathrm{^\circ C}$. Assuming steady-state is reached, how far into the glass sheet, from the high-temperature side, will the temperature be $+15 \; \mathrm{^\circ C}$.
I understand how to do the problem, I'm just having difficulty with unit correlation.
My first step was to calculate the heat flux. Since the system already reached steady-state I used the following equation: $q=-k \; \mathrm{d}T/\mathrm{d}x$. Then I used the value of $q$ to solve for how far into the glass the temperature will be $15 \; \mathrm{^\circ C}$ : $\Delta x=-k \Delta T/q$
My teacher posted the solutions and my steps were correct just not the values. $k$ is given to us $k=1.7 \; \mathrm{J/m\cdot k\cdot s}$, the temperature in degrees celsius and length in mm. I converted $2\; \mathrm{mm}$ to $0.002 \; \mathrm{m}$. But the solution posted did not correlate the units for temperature. I'm just confused why that is, shouldn't the $20 \; \mathrm{^\circ C}$ be converted to kelvin or vice versa? This way they will cancel out properly in the calculation.
Any help is greatly appreciated and I've attached a photo of the solution provided to us to make my question more clear. Thanks