Question

Three liquids A, B and C having same specific heats have masses m, 2m and 3m. Their temperatures are, $\theta ,2\theta and3\theta$ respectively. For temperature of mixture, match the following two columns.

Answer 1

Given - $m_1=m,m_2=2m,m_3=3m,t_1=\theta ,t_2=2\theta ,t_3=3\theta ,c_1=c_2=c_3=c$ ,

the final temperature of a mixture of $n$ liquids is given by ,

$t=\frac{m_1{c}_1{t}_1+m_2{c}_2{t}_2+...........+m_n{c}_n{t}_n}{m_1{c}_1+m_2{c}_2+........+m_n{c}_n}$ ,

(1) when A and B are mixed

hence , $t=\frac{mc\theta +2mc\times 2\theta }{mc+2mc}=5\theta /3$

(2) when A and C are mixed

hence , $t=\frac{mc\theta +3mc\times 3\theta }{mc+3mc}=5\theta /2$

(3) when B and C are mixed

hence , $t=\frac{2mc\times 2\theta +3mc\times 3\theta }{2mc+3mc}=13\theta /5$

(4) when A ,B and C are mixed

hence , $t=\frac{mc\theta +2mc\times 2\theta +3mc\times 3\theta }{mc+2mc+3mc}=7\theta /3$