A geyser heats water flowing at a rate of $$2.0$$ kg per minute from $$30°$$C to $$70°$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min$$^{-1}$$.
[Heat of combustion $$= 8 \times 10^3$$ J g$$^{-1}$$, Specific heat of water $$= 4.2$$ J g$$^{-1}$$ °C$$^{-1}$$]

We need to find the rate of combustion of fuel in a geyser that heats water.

Since the flow rate of water is $$2.0$$ kg/min (equivalent to $$2000$$ g/min), the temperature rise is $$70°$$C $$- 30°$$C = $$40°$$C, the heat of combustion is $$8 \times 10^3$$ J/g, and the specific heat of water is $$4.2$$ J g$$^{-1}$$ °C$$^{-1}$$, we first calculate the heat required per minute.

Using $$Q = m \times c \times \Delta T$$ gives $$Q = 2000 \times 4.2 \times 40 = 336000$$ J/min.

Now, if $$x$$ g of fuel is burnt per minute, then $$x \times 8 \times 10^3 = 336000$$. Substituting and solving yields $$x = \frac{336000}{8000} = 42$$ g/min.

The rate of combustion of fuel is 42 g min$$^{-1}$$.