A geyser heats water flowing at the rate of 3.0 liters per minute from 27°C to 77°C

A geyser heats water flowing at the rate of 3.0 liters 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?

Solutions

Expert Solution

Given data in the problem is:

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

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

Initial temperature, T1 = 27oC

Final temperature, T2 = 77oC

Rise in temperature, T = T2 – T1

= 77 – 27

= 50oC

Heat of combustion = 4 x 104 J / g

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

Mass of flowing water, m = 3.0 litre/min

= 3000 g/min

Total heat used, Q = mcT

= 3000 x 4.2 x 50

On calculation, we get,

= 6.3 x 105 J/min

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

We get,

= 15.75 g/min

Therefore, rate of consumption is 15.75 g/min.

The rate of consumption is 15.75 g/min.

Ajay Kumar Gupta answered 2 years ago

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