How Much Does a Teaspoon of Water Weigh?

Fermi Question

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Fermi Question

Question

If the mass of one teaspoon of water could be converted entirely into energy (Western University) in the form of heat, what volume (liters) of water, initially at room temperature, could it bring to a boil?

Solution

1 teaspoonful is equivalent to 5 mL.

For the case of water, it is 5 grams which is same as 0.005 kg

The equivalence energy level is given by;

E = mc² = (0.005) (3e8)²

= 4.5e14 joules or 450 TJ (Tera joules)

To "bring to a boil" implies that the temperature is increased to a level of 100ºC, but ensuring that none of it boils. In this case, we assume that room temperature is 25ºC.

The specific heat of water stands at 4.186 kJ/kgC

Therefore;

E = 4.5e14 J = 4186 J/kgC x m x (100–25)

E = mcΔT = M(4.2)(100 - 25) = 15 x 10^13 = 4.7 x 10^11 kg

Density of water = 1 kg/L

As a result, Volume of 4.7 x 10^11 kg water = 4.7 x 10^11 L

References

Bouffard, K. (1999). Fermi questions. The Physics Teacher, 37(5), 314-314.

Taggart, G. L., Adams, P. E., Eltze, E., Heinrichs, J., Hohman, J., & Hickman, K. (2007). Fermi questions. Mathematics Teaching in the Middle School, 13(3), 164-167.