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  4. 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 × 103 Jg -1 Specific heat of water =4.2 Jg -1 ° C -1 ]

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

JEE MainJEE Main 2022Thermal Properties of Matter

Solution:

$m =2000 gm / \min$
Heat required by water $/ \min = mS \Delta T$
$ =(2000) \times 4.2 \times 40 J / \min $
$=336000 J / \min$
The rate of combustion $=\left(\frac{ dm }{ dt } L \right)=336000 J / \min$
$\frac{ dm }{ dt }=\frac{336000}{8 \times 10^{3}} g / \min$
$=42 \,gm / \min$