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