Question

A tap supplies water at 26 degrees Celsius while other supplies water at 82 degrees. If a man wishes to bath with water at 40 degrees Celsius the ratio of the mass of hot water to that of cold water is?

Answer 1

To determine the ratio of the mass of hot water to that of cold water, we can use the principle of the conservation of energy.

Let's assume the mass of hot water as $m_h$ and the mass of cold water as $m_c$.

The initial temperature of the hot water, supplied at 82 degrees Celsius, is T_h = 82 , ^circ ext{C}. The initial temperature of the cold water, supplied at 26 degrees Celsius, is T_c = 26 , ^circ ext{C}. The desired final temperature of the mixture, when the man bathes, is T_f = 40 , ^circ ext{C}.

To calculate the ratio of the masses, we need to apply the principle of conservation of energy:

$m_h\cdot c\cdot (T_f-T_h)=m_c\cdot c\cdot (T_c-T_f)$,

where $c$ is the specific heat capacity of water (which is approximately 1 calorie per gram per degree Celsius).

Now, let's substitute the given values into the equation and solve for the ratio:

mh⋅1⋅(40−82)=mc⋅1⋅(26−40)m_h cdot 1 cdot (40 - 82) = m_c cdot 1 cdot (26 - 40)mh​⋅1⋅(40<span class="mspace" style="margi