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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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