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]

Solution

Physics sir · 3 steps

Heat taken by the water each minute must come from fuel burnt each minute. Balance the two per minute.

1. Heat to water. Each minute, 2.0 kg = 2000 g of water is heated through Δ T = 70 - 30 = 40 °C. Grams are needed because the specific heat is given per gram.

   Q/t = m/t s Δ T = 2000 × 4.2 × 40 = 3.36 × 10⁵ J min⁻¹

2. Heat from fuel. Each gram of fuel releases 8 × 10³ J. So the fuel burnt per minute is (3.36 × 10⁵)/(8 × 10³) = 42 g min⁻¹.
3. So. The gas burner must burn fuel at 42 g min⁻¹.

The common slip: 0.042. Putting the mass in as 2 instead of 2000 g gives 0.042, not 42. The specific heat is per gram, so the flow must be in grams too.

The idea to keep. For a steady-flow heater, work everything per unit time: (mass flow rate) times s Δ T equals (fuel burn rate) times heat of combustion. Match the mass units to the given constants first.

Answer from the NTA final answer key. Solution by PrepWiser.