If you wish to warm 52 kg of water by 22 ∘c for your bath, find what the quantity of heat is needed. express your answer in calories cal.

Given:

m = 52 kg. the mass of water

ΔT = 22 °C, the temperature increase

Note that

c = 4.184 J / (g-°C), the specific heat of water.

The quantity of heat required is

Q = mcΔT

= (52,000 g) * (4.184 J / (g-°C)) * (22 °C)

= 4.7865 x 10⁴ J

Because 1 J = 2.39 x 10⁻⁴ cal. the heat required is

Q = (4.7865 x 10⁴ J) * (2.39 x 10⁻⁴ cal/J) = 1143.97 cal ≈ 1144 cal

Answer: 1144 cal