In: Physics
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?
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.