- Home
- Standard 11
- Physics
A geyser heats water flowing at the rate of $3.0$ litres per minute from $27\,^{\circ} C$ to $77\,^{\circ} C$ If the geyser operates on a gas burner, what is the rate of consumption (in $g/min$) of the fuel if its heat of combustion is $4.0 \times 10^{4}\; J / g$ ?
$15.75$
$24.65$
$8.62$
$18.95$
Solution
Water is flowing at a rate of 3.0 litre/min.
The geyser heats the water, raising the temperature from $27^{\circ} C$ to $77^{\circ} C$.
Initial temperature, $T_{1}=27^{\circ} C$
Final temperature, $T_{2}=77^{\circ} C$
$\therefore$ Rise in temperature, $\Delta T=T_{2}-T_{1}$
$=77-27=50^{\circ} C$
Heat of combustion $=4 \times 10^{4} J / g$
Specific heat of water, $c=4.2 J g ^{-1} c C ^{-1}$
Mass of flowing water, $m=3.0$ litre/min $=3000 g / min$
Total heat used, $\Delta Q=m c \Delta T$
$=3000 \times 4.2 \times 50$
$=6.3 \times 10^{5} J / min$
$\therefore$ Rate of consumption $=\frac{6.3 \times 10^{5}}{4 \times 10^{4}}=15.75 \,g / min$