An immersion heater is rated 1500W. How long does it take the heater to raise the temperature of 1 kg of water…

Analyze the question: A 1500 W heater supplies energy at a steady rate. We need the time to heat 1 kg of water through a 30°C rise, with no heat lost.

Concept: Electrical energy supplied = heat gained by the water.

• Electrical energy: E = P × t
• Heat gained: Q = mcΔθ

So: P × t = mcΔθ

Solution:

Given: P = 1500 W, m = 1 kg, c = 4200 J kg⁻¹ K⁻¹, Δθ = 30°C

1. Heat needed: Q = 1 × 4200 × 30 = 126,000 J
2. Time: t = Q / P = 126,000 / 1500 = 84 s

Answer: A (84 s)

Tip: For any heater question with no heat loss, write P·t = mcΔθ right away. Then simplify before multiplying: 4200 × 30 / 1500 = 4200 / 50 = 84. Always check that your units are in kg, J and seconds before calculating.