An example of mixture type of problem

A 200-g block of copper at temperature of 90 C is dropped into 400 g of water at 27 C. The water is contained in a 300-g glass container. What is the final temperature of the mixture?

DE = DEcopper + DEwater + DEglass
= ccoppermcopper(T-Tcopperi) + cwatermwater(T-Twateri) + cglassmglass(T-Tglassi)
= 0

(ccoppermcopper + cwatermwater + cglassmglass) T
= ccoppermcopperTcopperi + cwatermwaterTwateri + cglassmglassTglassi

T = (ccoppermcopperTcopperi + cwatermwaterTwateri + cglassmglassTglassi)/
(ccoppermcopper + cwatermwater + cglassmglass)
= 30 C

In general, if one mixes any number of substances with the coldest at Tmin and hottest at Tmax, the equilibrium temperature of the mixture has to satisfy

Tmin T Tmax