A gas-based geyser heats water flowing at a rate of 5.0 litres per minute from 27°C to 87°C

A gas-based geyser heats water flowing at a rate of 5.0 litres per minute from 27°C to 87°C. Find the rate of consumption of gas (in g/s). Given: Heat of combustion of gas = (5.0 \times 10^4) J/g Specific heat of water = 4200 J/kg°C Options:

1. 2.1 g/s
2. 4.2 g/s
3. 0.42 g/s
4. 0.21 g/s

Solution:

Water flow rate: $[ \dot m = \dfrac{5}{60} = \frac{1}{12}\ \text{kg/s} ]$ Heat required per second: $[ P = \dot m c \Delta T = \dfrac{1}{12} \times 4200 \times 60 ]$ Let gas consumption = x g/s: $[ x(5\times10^4) = 21000 \Rightarrow x = 0.42\ \text{g/s} ]$ ✅ Correct Answer: (3)