Question

If you wish to warm 40 kg of water by 18 ∘C for your bath, find what the quantity of heat is needed. Express your answer in calories cal

Answer 1

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.

Answer 2

Quantity of heat needed (Q) = 722.753 × 10³

Step-by-step explanation:

According to question,

Mass of water (m) = 40 kg

Change in temperature ( ΔT) = 18°c

specific heat capacity of water = 4200 j kg^-1 k^-1

The specific heat capacity is the amount of heat required to change the temperature of 1 kg of substance to 1 degree celcius or 1 kelvin .

So, Heat (Q) = m×s×ΔT

Or, Q = 40 kg × 4200 × 18

or, Q = 3024 × 10³ joule

Hence, Quantity of heat needed (Q) = 3024 × 10³ joule

In calories 4.184 joule = 1 calorie

So, 3024 × 10³ joule = 722.753 × 10³