Question

Water is heated from ${10}^{\circ }C$ to ${90}^{\circ }C$ in a residential hot water heater at a rate of $70litre$ per minute. Natural gas with a density of $1.2kg/m^3$ is used in the heater, which has a transfer efficiency of $32\%$. if the gas consumption rate in cubic meters per hour is 13k. Then what is the value of k? (heat combustion for natural gas is $8400kcal/kg$)

Answer 1

$d_{gas}=$1.2 gm per $c{m}^3$

Heat combustion for natural gas: $8400$ $\frac{kcal}{kg}$

Efficiency: $32\%$

Hence, heat generated by combustion of natural gas : $1.2\times 8400\times 0.32=100.8\times 32$

Water is heated from ${10}^{0}C$ to ${90}^{0}C$ in a residential hot water heater at a rate of 70litre per minute.

Amount of heat used by water per hour is

$Q=70\times 60\times 1\times (90-10)$

Equating amount of heat of heat generated from combustion to heat used by heating

$100.8\times 32\times R=70\times 60\times 80$ where R is the gas consumption rate

$\therefore R=\frac{70\times 60\times 80}{100.8\times 32}=104.17=104.2$ kcal per kg