A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ}C$ to $8

Question

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ}C$ to $87^{\circ}C$.

The rate of consumption of the gas is $\_\_\_\_$ g/s.

(Take heat of combustion of gas $= 5.0 \times 10^{4}\text{ }J/g$ ) specific heat capacity of water $= 4200\text{ }J/kg.\ ^{\circ}C$

Accepted Answer

Water flow rate $= 5\mathcal{l}/min = \frac{5}{60}\text{ }kg/s$

∴ Power of heater $= \frac{dm}{dt}S\Delta T = \frac{1}{12} \times 4200 \times 60\text{ }W$

$\therefore\ $ Let rate of consumption of gas be $xg/s$.

$${\therefore\ x \times 5.0 \times 10^{4} = \frac{1}{12} \times 4200 \times 60 }{\Rightarrow \ x = 4200 \times 10^{- 4} = 0.42\text{ }g/s}$$

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