A geyser heats water flowing at a rate of $2.0 \mathrm{kg}$ per minute from $30°\mathrm{C}$ to $70°\mathrm{C}$. If geyser operates on a gas burner, the rate of combustion of fuel will be _____ $\mathrm{g} {\min }^{-1}$.

[Heat of combustion $=8\times {10}^3{\mathrm{Jg}}^{-1}$, Specific heat of water $=4.2{\mathrm{Jg}}^{-1}{{}^{\circ }\mathrm{C}}^{-1}$]

Given here, mass flow rate of water, $\frac{dm}{dt}=2 \mathrm{kg} {\min }^{-1}$

The geyser heats the water, raising the temperature from ${\theta }_1=30°\mathrm{C}$ to ${\theta }_2=70°\mathrm{C}$.

Total heat utilised in raising the temperature, $\frac{\Delta Q}{\Delta t}=\frac{dm}{dt}\times s\Delta \theta$

$\frac{\Delta Q}{\Delta t}=\frac{2}{60}\times 4.2\times 40=\frac{m}{t}\times L$

$L=$ heat of combination$=8\times {10}^3 \mathrm{J} {\mathrm{g}}^{-1}$

Now, rate of consumption of fuel is $\frac{m}{t}=\frac{2\times 4.2\times 40}{60\times 8\times {10}^3}$

$=\frac{4.2}{6}\times {10}^{-3}=0.7\times {10}^{-3} \mathrm{kg} {\sec }^{-1}$

$=42 \mathrm{g} {\min }^{-1}$