Question

A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 10⁴ J/g ?

Answer 1

Water is flowing at a rate of 3.0 litre/min. 

The geyser heats the water, raising the temperature from 27°C to 77°C. 

Initial temperature, T₁ = 27°C 

Final temperature, T₂ = 77°C 

∴Rise in temperature, ΔT = T ₂-T₁= 77 – 27= 50°C 

Heat of combustion = 4 × 10⁴ J/g

Specific heat of water, c = 4.2 J g ^-1°c^-1

Mass of flowing water, m = 3.0 litre/min = 3000 g/min 

Total heat used, ΔQ = mc ΔT 

= 3000 × 4.2 × 50 = 6.3 × 10⁵ J/min 

∴ Rate of consumption = \(\frac{6.3×10^5}{4×10^4}=15.75\) g/min