How much gas is required to heat 200 imperial gallons of water from 50°F to 150°F in a 90% efficient hot water heater?

How much gas is required to heat 200 imperial gallons of water from 50°F to 150°F in a 90% efficient hot water heater?

• A. 220 CF
• B. 110 CF
• C. 440 CF
• D. 180 CF

Answer: (A)

To heat water you need energy equal to the mass of the water times its specific heat capacity and the temperature rise. Start by turning the water amount into mass: 200 imperial gallons is about 200 × 4.546 liters ≈ 909 liters, and water’s density is about 1 kg/L, so the mass is roughly 909 kg. The temperature rise from 50°F to 150°F is about 10°C to 65.6°C, a ΔT of about 55.6°C. Heat required (in kJ) ≈ m × Cp × ΔT = 909 kg × 4.186 kJ/kg·K × 55.6 K ≈ 211,000 kJ. Converting to BTU (1 kJ ≈ 0.9478 BTU) gives roughly 200,000 BTU of heat needed. With a 90% efficient heater, the gas input energy must be about 200,000 BTU / 0.90 ≈ 222,000 BTU. Natural gas provides roughly 1,000 BTU per cubic foot, so the required gas volume is about 222,000 ÷ 1,000 ≈ 222 cubic feet. Rounding to the nearest practical value gives about 220 cubic feet.

To heat water you need energy equal to the mass of the water times its specific heat capacity and the temperature rise. Start by turning the water amount into mass: 200 imperial gallons is about 200 × 4.546 liters ≈ 909 liters, and water’s density is about 1 kg/L, so the mass is roughly 909 kg. The temperature rise from 50°F to 150°F is about 10°C to 65.6°C, a ΔT of about 55.6°C.

Heat required (in kJ) ≈ m × Cp × ΔT = 909 kg × 4.186 kJ/kg·K × 55.6 K ≈ 211,000 kJ. Converting to BTU (1 kJ ≈ 0.9478 BTU) gives roughly 200,000 BTU of heat needed.

With a 90% efficient heater, the gas input energy must be about 200,000 BTU / 0.90 ≈ 222,000 BTU.

Natural gas provides roughly 1,000 BTU per cubic foot, so the required gas volume is about 222,000 ÷ 1,000 ≈ 222 cubic feet. Rounding to the nearest practical value gives about 220 cubic feet.