Question

A hot body at temperature ${\theta }_1$ is mixed with a cold body at temperature ${\theta }_2$. The fall in temperature of the hot body is equal to the rise in temperature of the cold body. The material and the mass of both the bodies are same. Then find the resultant temperature.

Answer 1

Given: A hot body at temperature ${\theta }_1$ is mixed with a cold body at temperature ${\theta }_2$. The fall in temperature of the hot body is equal to the rise in temperature of the cold body. The material and the mass of both the bodies are same.

To find the resultant temperature.

Solution:

As per given condition,

Specific heat of both bodies are same as their materials are same, i.e., $s_1=s_2$

Mass of both bodies are same, i.e., $m_1=m_2$

Let the final temperature be $T$

Here Heat lost by hot water = Heat gained by hot boiling water

$m_1{s}_1({\theta }_1-T)=m_2{s}_2(T-{\theta }_2)⟹({\theta }_1-T)=T-{\theta }_2⟹2T={\theta }_1+{\theta }_2⟹T=\frac{{\theta }_1+{\theta }_2}{2}$

is the final temperature of the mixture.