Question

A geyser heats water flowing at the rate of 3 litres per minute from $27^{\circ} C$ to $77^{\circ} C$. If the geyser operates on a gas burner, and its heat of combustion is $4 \times 10^{4} J / g$, then the rate of consumption of fuel is

• A. 8 g per min
• B. 12 g per min
• C. 16 g per min
• D. 20 g per min

Answer 1

Answer: (C)

1 litre of water equals $1000 g$ of water.
$\Delta Q=m s \Delta T$
$\left(\frac{\Delta Q}{\Delta t}\right)=\left(\frac{m}{\Delta t}\right) s \Delta T$
As, $s_{\text {water }}=4.2 J g ^{-1}{ }^{\circ} C ^{-1}$
$\left(\frac{\Delta Q}{\Delta t}\right)=\frac{(3000 g )}{1 min }\left(4.2 J g ^{-1}{ }^{\circ} C ^{-1}\right)(77-27)^{\circ} C$
$\left(\frac{\Delta Q}{\Delta t}\right)=630000 J min ^{-1}$
As heat of combustion $(L)$
$L=\left(\frac{\Delta Q}{\Delta m}\right)=4 \times 10^{4} J g ^{-1}$
$\Rightarrow (L)\left(\frac{\Delta m}{\Delta t}\right)=630000 J min ^{-1}$
$\Rightarrow \frac{\Delta m}{\Delta t}=\frac{630000 J min ^{-1}}{4 \times 10^{4} J g ^{-1}} \approx 16 \,g \,min ^{-1}$