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, what is the rate of combustion of fuel (approx.), if its heat of combustion is $4\times {10}^{4}J/g$.

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

Answer 1

The correct option is B $16g/min$

Formula used: $M=V\rho ,Q=mc\Delta \theta$

Given: $V=3.0$ litre per minute , ${\theta }_i={27}^{\circ }C,{\theta }_f={77}^{\circ }C$, energy per gram $=4\times {10}^{4}J/g$.

Mass of water heated,
$m=3\times 1000=3000g/min$
Rise in temperature, $\Delta \theta =77–27={50}^{\circ }C$
Amount of heat spent, $Q=mc\Delta \theta$
$Q=3000\times 1\times 50cal/min$
$Q=3000\times 50\times 4.2J/min$
$Q=6.3\times {10}^{5}J/min\dots \left(i\right)$

Rate of combustion of fuel,
$\frac{Q}{\text{energy per gram}}=\frac{6.3\times {10}^5}{4.0\times {10}^4}=15.75g/min$
Rate of combustion of fuel $=15.75g/min\approx 16g/min$

FINAL ANSWER: (d).