Earthquake Physics-- From Magnitude to Megawatt--Conversion Equations

equation for converting a 7.0 magnitude earthquake to joules of energy

The energy released by an earthquake of magnitude $M$ on the Richter scale can be calculated using the equation:

$$\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">E</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">25</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">,</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">000</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10</span></span>}}^{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">1.5</span></span>}\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">M</span></span>}}\text{<span style="font-family: georgia;"><span style="font-size: medium;">(in joules)</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">[</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">1</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">]</span></span><span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">[</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">6</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">]</span></span><span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">[</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">7</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">]</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">.</span></span>}$$

For a magnitude 7.0 earthquake, substitute $M=7.0$ into the formula:

$$\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">E</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">25</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">,</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">000</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10</span></span>}}^{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">1.5</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\cdot </span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">7.0</span></span>}}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">25</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">,</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">000</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10</span></span>}}^{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10.5</span></span>}}\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">.</span></span>}$$

Simplifying further:

$$\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">E</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">25</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">,</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">000</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\cdot </span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">3.162</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\times </span></span>{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10</span></span>}}^{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10</span></span>}}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">7.905</span></span>}<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">\times </span></span>{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">10</span></span>}}^{\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">14</span></span>}}\text{<span style="font-family: georgia;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="font-family: georgia;"><span style="font-size: medium;">joules</span></span>}\mathrm{<span\; style="font-family:\; georgia;"><span\; style="font-size:\; medium;">.</span></span>}$$

Thus, a magnitude 7.0 earthquake releases approximately $7.9\times {10}^{14}$ joules of energy.

https://www.perplexity.ai/search/equation-for-converting-a-7-0-U46eDAyRTeijiStUPxf2HA

convert 7.9×10 (^14) joules to megawatt hours

To convert $7.9\times {10}^{14}$ joules to megawatt-hours (MWh), use the formula:

$$\text{MWh}=\frac{\text{Joules}}{3,600,000,000}$$

Calculation:

$$\text{MWh}=\frac{7.9\times {10}^{14}}{3.6\times {10}^9}=2.1944\times {10}^5\text{MWh}$$

Final Answer:

$7.9\times {10}^{14}$ joules is equal to 219,440 MWh

https://www.perplexity.ai/search/convert-7-9x10-14-joules-to-me-Vvq1obAWRIWPnZdG8noSsQ

how many households would 219,440 MWh service

how many households would 219,440 MWh service

To determine how many households 219,440 MWh of electricity could service, we need to consider the average annual electricity consumption per household. In the United States, the average household consumes approximately 10,632 kWh per year (based on recent U.S. Energy Information Administration data).

Using this figure:

$$\text{Number of households}=\frac{\text{Total MWh}}{\text{Average household consumption in MWh}}$$

Converting average household consumption to MWh:

$$10,632\text{kWh/year}=10.632\text{MWh/year}$$

Now calculate:

$$\text{Number of households}=\frac{219,440}{10.632}\approx 20,645$$

Thus, 219,440 MWh could service approximately 20,645 households for one year.

https://www.perplexity.ai/search/how-many-households-would-2194-V7ISX3ZKSm.WXJr79EQ_og

(X:) https://x.com/jameslangelle