Question

You need to boil 12.5 L of water using your natrual gas (primarily methane) stove. What volume of natural gas is needed to boil the water if only 15.6% of the heat generated goes towards heating the water. Assume the density of methane is 0.660g/L , the density of water is 1.00 g/mL , and that the water has an initial temperature of 23.4 °C

Answer 1

Energy required for boiling of $12.5 L$ of water:

1. \ Energy required to increase it's temperature from $23.4\degree C\to100\degree C$

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

$=mC(T_2-T_1)+mL_v=$ $12.5 \times 4.184\times (100-23.4)+12.5\times 2256=$ $32206.18KJ$

Let $V$ be the volume of methane required,

Mass of methane will be$=d\times V=0.66V g$ (where d is the density)

Calorific value of methane$=55KJ/g$

$15.6$ % of Total energy of methane $=$ $32206.18 KJ$

$\implies \frac{15.6}{100}\times 55\times 0.66\times V=32206.18$

$V=5687.32 L$