question_answer

Two bodies of specific heats \[{{c}_{1}}\] and \[{{c}_{2}}\] having same heat capacities are combined to form a single composite body. What is the specific heat of the composite body?

Answer:

                As the heat capacities are equal, so \[{{m}_{1}}{{c}_{1}}={{m}_{2}}{{c}_{2}}\]. Let c be the specific heat of the composite body. Then \[({{m}_{1}}+{{m}_{2}})c={{m}_{1}}{{c}_{1}}+{{m}_{2}}{{c}_{2}}={{m}_{1}}{{c}_{1}}+{{m}_{1}}{{c}_{1}}=2{{m}_{1}}{{c}_{1}}\] or \[c=\frac{2{{m}_{1}}{{c}_{1}}}{{{m}_{1}}+{{m}_{2}}}=\frac{2{{m}_{1}}{{c}_{1}}}{{{m}_{1}}+{{m}_{1}}\frac{{{c}_{1}}}{{{c}_{2}}}}\] \[=\frac{2{{c}_{1}}{{c}_{2}}}{{{c}_{1}}+{{c}_{2}}}\].