The chocolate crumb mystery.Explosions ignited by electrostatic discharges (sparks) constitute a serious danger in facilities handling grain or powder. Such an explosion occurred in chocolate crumb powder at a biscuit factory in the 1970s. Workers usually emptied newly delivered sacks of the powder into a loading bin, from which it was blown through electrically grounded plastic pipes to a silo for storage. As part of the investigation of the biscuit factory explosion, the electric potentials of the workers were measured as they emptied sacks of chocolate crumb powder into the loading bin, stirring up a cloud of the powder around themselves. Each worker had an electric potential of about 7.0kVrelative to the ground, which was taken as zero potential.(a)Assuming that each worker was effectively a capacitor with a typical capacitance of 200pF, find the energy stored in that effective capacitor. If a single spark between the worker and any conducting object connected to the ground neutralized the worker, that energy would be transferred to the spark. According to measurements, a spark that could ignite a cloud of chocolate crumb powder, and thus set off an explosion, had to have energy of at least150mJ. (b)Could a spark from a worker have set off an explosion in the cloud of powder in the loading bin?

Step by step solution

01

The given data

1. Electric potential of worker relative to ground, V=7 kV
2. Capacitance, C = 200 pF
3. Energy required for explosion, U = 150 mJ

02

Understanding the concept of the stored energy

The energy stored in the effective capacitor is directly proportional to the capacitance. By using this equation, we can find the energy stored in the capacitor. For the explosion, the required energy is. So, from our result, we conclude whether the spark occurred or not.

Formula:

The energy stored within the capacitor plates, $U=\frac{1}{2}C{V}^2$ …(i)

03

(a) Calculation of the stored energy in the effective capacitor

The energy stored in the effective capacitor can be calculated using the given data in equation (i) as follows:

$$\begin{gathered} U=\frac{1}{2}\times \left(200\times {10}^{-12}\mathrm{F}\right)\times {\left(7\times {10}^3\mathrm{V}\right)}^2 \\ =\left(1\times {10}^{-10}\mathrm{F}\right)\times \left(49\times {10}^6{\mathrm{V}}^2\right) \\ =4.9\times {10}^{-3}\mathrm{J} \end{gathered}$$

Hence, the value of the stored energy is $4.9\times {10}^{-3}J$.

04

(b) Calculation for the reason if a spark from the worker can cause explosion

But from the given condition for the spark to occur, we require energy

From the calculations of part (a), we can conclude that the energy is very small.

Hence, such a spark shouldn’t have set off an explosion.

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