Question

A geyser uses natural gas as fuel. It heats water flowing at the rate of 3.0 liters per minute from 27°C to 77°C. The approximate rate of consumption of the fuel, if the heat of combustion of gas fuel is \(4.0 \times 10^4 { J/g}^{-1}\):

• A. \(3.75 { g/min}^{-1}\)
• B. \(0.9 { g/min}^{-1}\)
• C. \(1.5 { g/min}^{-1}\)
• D. \(16 { g/min}^{-1}\)

Hint:

Ensure conversion factors and efficiencies are considered in practical applications to understand differences between theoretical and actual fuel consumption.

Answer 1

The Correct Option is D

Step 1: Calculate the energy required to heat the water. 
The specific heat capacity of water \( C \) is approximately \( 4.18 { J/g°C} \), and the mass of water heated per minute is \( 3000 { g} \) (since \( 1 { liter} \approx 1000 { g} \)). Energy required \( Q \) to heat the water: \[ Q = mC\Delta T = 3000 { g} \times 4.18 { J/g°C} \times (77 - 27) { °C} = 627000 { J}. \] Step 2: Calculate the mass of gas required. 
Using the heat of combustion: \[ {Mass of gas} = \frac{Q}{{Heat of combustion}} = \frac{627000 { J}}{4.0 \times 10^4 { J/g}^{-1}} \approx 15.675 { g/min}. \] The answer is rounded or adjusted to \(16 { g/min}^{-1}\) to match the option provided, suggesting typical usage rates and efficiency considerations might lead to this value.