Question

For taking a bath, water at 40'C is required. Calculate the mass of cold water at 15'C which is to be added to 60 kg water at 100'C for bathing purpose?

Answer 1

Answer:

60kg + 40kg = 100kg......

Answer 2

Answer:

The mass of cold water required is 144 kg.

Explanation:

We will use the principle of calorimetry to solve this question. The principle of calorimetry states that the heat lost by hot the body is equal to the total heat gained by the cold body. It is based on the law of conservation of energy. i.e.

Heat lost = Heat gained

$m_1c(t-t_1)=m_2c(t_2-t)$      (1)

Where,

m₁=mass of the cold water

t=required temperature

t₁=temperature of cold water

m₂=mass of hot water

t₂=temperature of hot water

c=specific heat capacity of water

The values given in the question are,

t=40° C

t₁=15°C

m₂=60kg

t₂=100°C

By substituting these values in equation (1) we get;

$m_1c(40\textdegree C-15\textdegree C)=60c(100 \textdegree C-40\textdegree C)$

$m_1\times 25\textdegree C=60 \times 60 \textdegree C$

$m_1 =\frac{60 \times 60 \textdegree C}{25\textdegree }=144kg$

Hence, the mass of cold water required is 144 kg.