Example 1:  How much heat (in Joules) is required to raise the temperature of A kg of water from T₁ (in C) to T₂ (in C)?

We use a definition and dimensional analysis:

The definition: 1 kcal is the amount of heat needed to raise 1 kg of water by 1 degree centigrade.

The dimensional analysis:

(A kg)(T₂ C - T₁ C)(1 kcal/(1 kg)(1⁰ C)(4186 J/1 kcal) = answer in Joules