Question

A mass $m_1$ of a substance of specific heat capacity $c_1$ at temperature $t_1$ is mixed with a mass $m_2$ of other substance of specific heat capacity $c_2$ at a lower temperature $t_2$.Deduce the expression for the temperature t of the mixture.State the assumption made,if any.

Answer 1

Assuming that no heat is lost to the surrounding;
Heat lost by hot body = Heat gained by cold body.

Given, Heat lost by hot body = $m_1\times c_1\times (t_1-t)$
(because $t_1$ is at higher temperature)

And Heat gained by cold body = $m_2\times c_2\times (t-t_2)$

Now,
$m_1\times c_1\times (t_1-t)$ =$m_2\times c_2\times (t-t_2)$