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XerxesZorgon/Fermi_Worksheet.sm

Created April 8, 2023 18:35
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SMath Studio worksheet for a Fermi problem
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Fermi_Worksheet.sm
<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="1.0.8348.30405"?>
<worksheet xmlns="http://smath.info/schemas/worksheet/1.0">
<settings ppi="96">
<identity>
<id>bf3528df-15d5-4841-be55-5d56f11fe1fa</id>
<revision>6</revision>
</identity>
<calculation>
<precision>4</precision>
<exponentialThreshold>5</exponentialThreshold>
<trailingZeros>false</trailingZeros>
<significantDigitsMode>false</significantDigitsMode>
<roundingMode>0</roundingMode>
<approximateEqualAccuracy>0</approximateEqualAccuracy>
<fractions>decimal</fractions>
</calculation>
<pageModel active="false" viewMode="2" printGrid="false" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
<paper id="1" orientation="Portrait" width="850" height="1100" />
<margins left="39" right="39" top="49" bottom="49" />
<header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
<footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
<backgrounds />
</pageModel>
<dependencies>
<assembly name="SMath Studio Desktop" version="1.0.8348.30405" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
<assembly name="MathRegion" version="1.11.8348.30405" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
<assembly name="TextRegion" version="1.11.8348.30405" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
</dependencies>
</settings>
<regions type="content">
<region left="198" top="9" width="370" height="38" color="#000000" fontSize="20">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<p style="font-size: 20px; font-weight: bold;">Solution to a Fermi Problem</p>
</content>
</text>
</region>
<region left="27" top="45" width="731" height="38" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<p>Problem: If the mass of one teaspoon of water could be converted entirely into energy in the form of heat, what volume of water, initially at room temperature, could it bring to a boil?</p>
</content>
</text>
</region>
<region left="117" top="90" width="203" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Convert teaspoons to liters</li>
</ul>
</content>
</text>
</region>
<region left="117" top="117" width="162" height="41" color="#000000" fontSize="10">
<math optimize="2">
<input>
<e type="operand">tsp2liter</e>
<e type="operand">1</e>
<e type="operand">202.884</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">:</e>
</input>
</math>
</region>
<region left="117" top="153" width="88" height="50" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">ρ</e>
<e type="operand">997</e>
<e type="operand" style="unit">kg</e>
<e type="operand" style="unit">m</e>
<e type="operand">3</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
</math>
</region>
<region left="225" top="162" width="110" height="23" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<p>Density of water</p>
</content>
</text>
</region>
<region left="117" top="198" width="209" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Mass of water per teaspoon</li>
</ul>
</content>
</text>
</region>
<region left="117" top="216" width="282" height="42" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">m</e>
<e type="operand">ρ</e>
<e type="operand">tsp2liter</e>
<e type="operator" args="2">*</e>
<e type="operand">1</e>
<e type="operand">1000</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">*</e>
<e type="operand" style="unit">m</e>
<e type="operand">3</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
<result action="numeric">
<e type="operand">0.0049</e>
<e type="operand" style="unit">kg</e>
<e type="operator" args="2">*</e>
</result>
</math>
</region>
<region left="117" top="252" width="425" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Use Einstein's equation to find the energy in a teaspoon of water</li>
</ul>
</content>
</text>
</region>
<region left="117" top="279" width="190" height="33" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">E</e>
<e type="operand">m</e>
<e type="operand" style="unit">c</e>
<e type="operand">2</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
<result action="numeric">
<e type="operand">4.4166</e>
<e type="operand">10</e>
<e type="operand">14</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
<e type="operand" style="unit">J</e>
<e type="operator" args="2">*</e>
</result>
</math>
</region>
<region left="117" top="315" width="415" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Energy required to increase one kilogram of water 75 degree K</li>
</ul>
</content>
</text>
</region>
<region left="117" top="342" width="113" height="41" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">c.p</e>
<e type="operand">4184</e>
<e type="operand" style="unit">J</e>
<e type="operand" style="unit">kg</e>
<e type="operand" style="unit">K</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
</math>
</region>
<region left="252" top="351" width="146" height="23" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<p>Heat capacity of water</p>
</content>
</text>
</region>
<region left="117" top="387" width="74" height="24" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">ΔT</e>
<e type="operand">75</e>
<e type="operand" style="unit">K</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
</math>
</region>
<region left="117" top="405" width="202" height="42" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">E.1</e>
<e type="operand">c.p</e>
<e type="operand">ΔT</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
<contract>
<e type="operand" style="unit">J</e>
<e type="operand" style="unit">kg</e>
<e type="operator" args="2">/</e>
</contract>
<result action="numeric">
<e type="operand">3.138</e>
<e type="operand">10</e>
<e type="operand">5</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
</result>
</math>
</region>
<region left="117" top="450" width="309" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Energy required to boil one kilogram of water</li>
</ul>
</content>
</text>
</region>
<region left="117" top="477" width="135" height="42" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">E.2</e>
<e type="operand">2.26</e>
<e type="operand">10</e>
<e type="operand">6</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
<e type="operand" style="unit">J</e>
<e type="operand" style="unit">kg</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">*</e>
<e type="operator" args="2">:</e>
</input>
</math>
</region>
<region left="117" top="522" width="463" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Quantity of water boiled (in kilograms) using energy from one teaspoon</li>
</ul>
</content>
</text>
</region>
<region left="117" top="549" width="215" height="48" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">Q.kg</e>
<e type="operand">E</e>
<e type="operand">E.1</e>
<e type="operand">E.2</e>
<e type="operator" args="2">+</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">:</e>
</input>
<result action="numeric">
<e type="operand">1.716</e>
<e type="operand">10</e>
<e type="operand">8</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
<e type="operand" style="unit">kg</e>
<e type="operator" args="2">*</e>
</result>
</math>
</region>
<region left="117" top="594" width="188" height="25" color="#000000" fontSize="10">
<text lang="eng" fontFamily="Arial" fontSize="10">
<content>
<ul>
<li>Convert mass to volume</li>
</ul>
</content>
</text>
</region>
<region left="117" top="612" width="186" height="47" color="#000000" fontSize="10">
<math>
<input>
<e type="operand">V</e>
<e type="operand">Q.kg</e>
<e type="operand">ρ</e>
<e type="operator" args="2">/</e>
<e type="operator" args="2">:</e>
</input>
<result action="numeric">
<e type="operand">1.7212</e>
<e type="operand">10</e>
<e type="operand">5</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
<e type="operand" style="unit">m</e>
<e type="operand">3</e>
<e type="operator" args="2">^</e>
<e type="operator" args="2">*</e>
</result>
</math>
</region>
</regions>
</worksheet>
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