Equal volumes of three liquids of densities `rho_1`,`rho_2` and `rho_3`, specific heat capacities `c_1,c_2` and `c_3` and temperatures `t_1,t_2` and `t_3`, respectively are mixed together. What is the temperature of the mixture? Assume no changes in volume on mixing.

Explanation

Let t be the temperature of the mixture.
Net loss of heat by all
`=(vrho_1)c_1(t_1-t)+(Vrho_2)c_2(t_2-t)+(Vrho_3)c_3(t_3-t)`
but net loss`=0`
`Vrho_1c_1(t_1-t)+Vrho_2c_2(t_2-t)+Vrho_3c_3(t_3-t)=0`
or `t=(rho_1c_1t_1+rho_2c_2t_2+rho_3c_3t_3)/(rho_1c_1+rho_2c_2+rho_3c_3)`