Question #171273

Suppose a boil water notice is sent out advising all residents in the area to boil their water before drinking it or using it for cooking. You need to boil 11.5 L

11.5 L of water using your natural gas (primarily methane) stove. What volume of natural gas is needed to boil the water if only 17.1%

17.1% of the heat generated goes towards heating the water. Assume the density of methane is 0.668 g/L

0.668 g/L, the density of water is 1.00 g/mL

1.00 g/mL, and that the water has an initial temperature of 21.0 °C

21.0 °C. Enthalpy of formation values can be found in this table. Assume that gaseous water is formed in the combustion of methane.

Expert's answer

Energy required for boiling of "11.5 L" of water:

"1. \\" Energy required to increase it's temperature from "21\\degree C\\to100\\degree C"

"2. \\" Energy required for boiling(Latent heat of evaporation)

"=mC(T_2-T_1)+mL_v=" "11.5 \\times 4.184\\times (100-21)+11.5\\times 2256=" "29745.16J"

Let "V" be the volume of methane required,

Mass of methane will be"=d\\times V=0.668V g" (where d is the density)

Calorific value of methane"=55KJ\/g"

"17.1" % of Total energy of methane "=" "29745.16J"

"\\implies \\frac{17.1}{100}\\times 55000\\times 0.668\\times V=29745.16J"

"V=4.73L"

"V=4.73L"

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