Question

A geyser heats water flowing at the rate of $3.0$ litre per minute from $27^{\circ} C$ to $77^{\circ} C$. If the geyser operates on a gas burner and its heat of combustion is $4.0 \times 10^{4} J / g$, then what is the rate of combustion of fuel (approx.)?

• A. 24 g/min
• B. 12 g/min
• C. 32 g/min
• D. 16 g/min

Answer 1

Answer: (D)

Mass of water heated,
$M=3 \times 1000 \times 1=3000\, g / \min$
Rise in temperature, $\Delta T=77-27=50^{\circ} C$
Amount of heat spent, $Q=m c \Delta T$
or $Q =3000 \times 1 \times 50\, cal$
$=3000 \times 50 \times 4.2\, J / \min$
$=6.3 \times 10^{5} J / \min$
Rate of combustion of fuel
$=\frac{6.3 \times 10^{5} J / \min }{4.0 \times 10^{4} J / g }$
$=15.75\, g / \min \approx 16\, g / \min$