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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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Solution to a Fermi Problem

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?

• Convert teaspoons to liters
[/itex] [itex] ρ 997 kg m 3 ^ / * : [/itex]

Density of water

• Mass of water per teaspoon
[itex] m ρ tsp2liter * 1 1000 / * m 3 ^ * : 0.0049 kg * [/itex]
• Use Einstein's equation to find the energy in a teaspoon of water
[itex] E m c 2 ^ * : 4.4166 10 14 ^ * J * [/itex]
• Energy required to increase one kilogram of water 75 degree K
[itex] c.p 4184 J kg K * / * : [/itex]

Heat capacity of water

[itex] ΔT 75 K * : [/itex] [itex] E.1 c.p ΔT * : J kg / 3.138 10 5 ^ * [/itex]
• Energy required to boil one kilogram of water
[itex] E.2 2.26 10 6 ^ * J kg / * : [/itex]
• Quantity of water boiled (in kilograms) using energy from one teaspoon
[itex] Q.kg E E.1 E.2 + / : 1.716 10 8 ^ * kg * [/itex]
• Convert mass to volume
[itex] V Q.kg ρ / : 1.7212 10 5 ^ * m 3 ^ * [/itex]