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# A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 x 10^4 J/g ?

Q12.1 A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is $4.0\times 10^4\ J/g$?

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The volumetric flow of water is

$\\\frac{dV}{dt}=3\ litres\ minute^{-1}\\$

Density of water = 1000 g/litre

The mass flow rate of water is

$\\\frac{dm}{dt}=\rho \frac{dV}{dt}\\ \frac{dm}{dt}=3000\ g\ min^{-1}$

Specific heat of water, c = 4.2 J g-1 oC-1

The rise in temperature is $\Delta T=77-27=50\ ^{o}C$

Rate of energy consumption will be

$\\\frac{dQ}{dt}=\frac{dm}{dt}c\Delta T\\ \frac{dQ}{dt}=3000\times 4.2\times 50\\ \frac{dQ}{dt}=6.3\times 10^{5}\ J\ min^{-1}$

The heat of combustion of fuel $=4.0\times 10^{4}J/g$

Rate of consumption of fuel is

$\\\frac{6.3\times 10^{5}}{4\times 10^{4}}\\ =15.75\ g\ min^{-1}$

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