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?
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Answer 1

Explanation:

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 = T2 – 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 = 6.3 × 105 / (4 × 104) = 15.75 g/min.

Answer 2

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 = T2 – 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 = 6.3 × 105 / (4 × 104)  =  15.75 g/min.