A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If geyser operates on a gas burner, the rate of combustion of fuel will be __________ g min–1. [Heat of combustion = 8 × 103 Jg–1, Specific heat of water = 4.2 Jg–1 °C–1]
To determine the rate of combustion of fuel needed for the geyser, follow these steps:
Step 1: Calculate Heat Required The water is heated from 30°C to 70°C, a change of 40°C. Using the formula for heat transfer, Q = mcΔT, where:
m = 2.0 kg = 2000 g (mass of water per minute)
c = 4.2 Jg-1°C-1 (specific heat of water)
ΔT = 40°C (temperature change)
Q = 2000 g × 4.2 Jg-1°C-1 × 40°C = 336,000 J
Step 2: Calculate Fuel Combustion Rate Given the heat of combustion is 8 × 103 Jg-1, use Q = mfuel × Heat of combustion to find mfuel (fuel mass per minute):
mfuel = Q / Heat of combustion = 336,000 J / 8,000 Jg-1 = 42 g
Step 3: Validate against Range The calculated rate of combustion, 42 g min-1, lies within the specified range of 42,42.
Therefore, the rate of combustion of fuel required is 42 g min-1.
