Question

A liquid of mass $m$ and specific heat $c$ is heated to a temperature $2T$. Another liquid of mass $\frac{m}{2}$ and specific heat $2c$ is heated to a temperature $T$. If these two liquids are mixed, the resulting temperature of the mixture is

• A. $\left(\frac{2}{3}\right)T$
• B. $\left(\frac{8}{5}\right)T$
• C. $\left(\frac{3}{5}\right)T$
• D. $\left(\frac{3}{2}\right)T$

Answer 1

The correct option is D $\left(\frac{3}{2}\right)T$

Heat absorbed by cooler system = heat released by hotter system
Let final temperature of the mixture at equilibrium be t

Then, $mc(2T-t)=\frac{m}{2}2c(t-T)$
$\Rightarrow t=\frac{3T}{2}$