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Home » 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?
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?
CBSE | Class 11 | NCERT | Thermodynamics
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?

Solution:

Given
The water is moving at a rate of 3.0 litres per minute.
The geyser heats the water, elevating the temperature from 27 degrees Celsius to 77 degrees Celsius as a result.

Initial temperature, T1 = 270 C

Final temperature, T2 = 770 C

Rise in temperature, T = T2 – T1

T= 77 – 27

T= 500 C

Heat of combustion = 4 x 104 J / g

Specific heat of water, C = 4.2 J / g 0C

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

Using Total heat , Q = mcT

Q= 3000 x 4.2 x 50

On evaluating, we get,

Q= 6.3 x 105 J / min

Rate of consumption = 6.3 x 105 / (4 x 104)

On solving we get, = 15.75 g/min

Therefore, rate of consumption is 15.75 g/min

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