Two liquids of equal volume are throughly mixed. If their specific heat are $C_1, C_2$, temperatures $ \theta_1, \theta_ 2$ and densities $d_1, d_2$ respectively. What is the final temperature of the mixture ?
$ mC_1 ( \theta_1 - \theta_e ) = m C_2 ( \theta_e - \theta_2 ) $ $ Vd_1C_1 ( \theta_1 - \theta_e) = Vd_2 C_2( \theta_e - \theta_2) $ $ \Rightarrow d_1 c_1 \theta_1 -(d_1c_1) \theta_e = (d_2 c_2) \theta_e - d_2 c_2 \theta_2 $