Talk:Rainbow Dash/@comment-26007558-20140504184859/@comment-1142365-20140504225325

Assume that all of Spike's heat is being conducted by the doorknob, so we can use the following:

$$\frac{\Delta Q}{\Delta t} = -kA \cdot \frac{\Delta \theta}{\Delta x} (1)$$

Where $$\frac{\Delta Q}{\Delta t}$$ is the rate of heat energy transfer, $$k$$ is the thermal conductivity, $$A$$ is the area over which the heat energy is transferred, $${\Delta \theta}$$ is the difference in temperature (this is what we want to find) and $${\Delta x}$$ is the thickness of the material.

$$\Delta Q$$ is the heat energy input required to melt the steel. So using:

$$\Delta Q = mc \cdot \Delta T (2)$$

Where $$c$$ is the specific heat capacity of iron, $$\Delta T$$ is increase in temperature of the material, and $$m$$ is the mass.

We'll take $$m$$ as being no more than 0.5kg. The melting temperature of medium-carbon steel is 1427 Celsius, so assuming the lock is already at room temperature, $$\Delta T$$ is roughly 1400. The specific heat capacity of medium-carbon steel is 0.49 kJ/kg/K. Therefore:

$$\Delta Q = 0.5 \cdot 1400 \cdot 0.49 = 343kJ$$

From the episode, Spike melts the lock in around 1 second. Therefore, going back to equation (1), $$\frac{\Delta Q}{\Delta t} = 343000$$. The thermal conductivity of medium-carbon steel is around 51 W/m.K. The area of the lock can be modelled as a square of length 0.1m, and the thickness can be said to be roughly 0.02m (this is a pretty hefty lock). Therefore:

$$343000 = -51 \cdot 0.1^2 \cdot \frac{\Delta \theta}{0.02}$$

$$\Delta \theta = -\frac{343000 \cdot 0.02}{51 \cdot 0.01}$$

$$\Delta \theta = -13500K (3sf)$$

So therefore the temperature of Spike's fire is around 13000 degrees Celsius... rather hot.