A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm

Question

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm{C}$ to $87^{\circ} \mathrm{C}$. The rate of consumption of the gas is $\_\_\_\_$ $\mathrm{g} / \mathrm{s}$. (Take heat of combustion of gas $=5.0 	imes 10^4 \mathrm{~J} / \mathrm{g}$ ) specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$

Professor PC Thomas Classes · Answer

Rate of flow of water is $\frac{dm}{dt} = 5 	ext{ kg/min} = \frac{5}{60} 	ext{ kg/s} = \frac{1}{12} 	ext{ kg/s}$. The heat required per second to raise the temperature is $\frac{dH}{dt} = \frac{dm}{dt} c \Delta T = \left(\frac{1}{12}ight) 	imes 4200 	imes (87 - 27) = 21000 	ext{ J/s}$. The rate of consumption of gas is $\frac{dH/dt}{	ext{Heat of combustion}} = \frac{21000 	ext{ J/s}}{5.0 	imes 10^4 	ext{ J/g}} = \frac{21}{50} 	ext{ g/s} = 0.42 	ext{ g/s}$.