There is a cube in a room, experiencing heat transfer through all of its faces. The initial temperature of the cube is $20$ degrees and the temperature of the environment is $5$ degrees. I need to work out the temperature of the cube after $600$ seconds.
The constant coefficients of the faces are: $0.001$ through $4$ of the faces, $0.005$ through $1$ of them, and $0.0015$ through the other.
I started by forming a differential equation, where $T$ is the temperature of the cube:
$$\frac{dT}{dt} = - ( 0.005(T-5)+0.0015(T-5) + 4 (0.001(T-5)))$$
I think the answer is either around $10.25$ degrees or $17.9$ degrees as I created a programme to estimate it using Euqler's Rule. Does anyone have a programme to verify which answer seems most reasonable or can solve it and tell me which seems most reasonable ?
We could lump the constants together $$ \frac{T-5}{20-5}=e^{ -\frac14 ( 0.0005+ 0.0015+4* 0.001)} $$