Final answer:
The quantity of heat needed to warm 40 kg of water by 18 °C is 720,000 calories.
Step-by-step explanation:
To calculate the quantity of heat needed to warm 40 kg of water by 18 °C, we use the formula Q = m × c × ΔT, where:
m is the mass of the water,
c is the specific heat capacity of water,
ΔT is the change in temperature.
For water, the specific heat capacity, c, is 4.184 joules per gram per degree Celsius (J/g°C) or 1 calorie per gram per degree Celsius (cal/g°C). Since there are 1,000 grams in a kilogram, we first convert the mass of water to grams: 40 kg × 1,000 g/kg = 40,000 g. The change in temperature, ΔT, is 18 °C.
Therefore, Q = 40,000 g × 1 cal/g°C × 18 °C = 720,000 calories (cal). The quantity of heat needed is 720,000 calories.