Heat Transfer — Heating a Pool (Worked Example)

Given

• m = 50,000 kg

• c = 4186 J/(kg·K)

• ΔT = 2.0 K

Find

The heat required Q.

Principle

Water's huge specific heat makes Q = mcΔT enormous for pools — heating them is expensive.

Formula

Solution

1. Substitute: $Q = (50000)(4186)(2.0)$

2. Note: Celsius degrees and kelvin increments are identical for temperature differences

3. Multiply: $Q = 4.186 \times 10^8\ \mathrm{J}$

Unit check

kg × J/(kg·K) × K = J. Mass × specific heat × ΔT yields energy — correct.

What this means physically

419 MJ — about 116 kWh of electricity, costing real money. This is why pool heaters run for days and solar covers help enormously.