JEE MAIN - Physics (2022 - 26th June Evening Shift - No. 21)
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 $$\times$$ 103 Jg$$-$$1, Specific heat of water = 4.2 Jg$$-$$1 $$^\circ$$C$$-$$1]
Answer
42
Explanation
$$Q = ms\Delta T$$
$${{dQ} \over {dt}} = {\left( {{{dm} \over {dt}}} \right)_{water}}S\Delta T = {\left( {{{dm} \over {dt}}} \right)_{oil}}C$$
$$ \Rightarrow 2 \times 4.2 \times {10^3} \times 40 = {\left( {{{dm} \over {dt}}} \right)_{oil}} \times 8 \times {10^6}$$
$$ \Rightarrow {\left( {{{dm} \over {dt}}} \right)_{oil}} = {{8 \times 4.2 \times {{10}^4}} \over {8 \times {{10}^6}}}$$ kg/minute
= 42 g/min
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