Question

Two bodies of specific heats C1 and C2 having same heat capacities are combined to form a single composite body. What is the specific heat of the composite body ?

Answer 1

Hi 

Here is your answer,

As the heat capacities are equal , so m₁C₁ = m₂C₂

Let C be the specific heat of the composite body. Then,

(m₁ + m₂) C = m₁C₁ + m₂C₂ 

    = m₁C₁ + m₁C₁ = 2 m₁C₁

        C = 2 m₁C₁/m₁+ m₂ = 2 m₁C₁/ m₁ + m₁ + m₁ C₁/C₂

         = 2 C₁C₂/C₁ + C₂




Hope it helps you !

Answer 2

Specific heats of two bodies m1 and m2 are C₁ and C₂ respectively.

The have equal heat capacity.

Heat capacity = mass * specific heat
             m₁ * C₁ = m₂ * C₂    --- (1)
       => m₂ = m₁ C₁ / C₂          ---(2)

The two bodies are combined (mixed physically and not chemically) to form a single body.

Total heat capacity of the combined body = 
    = m₁ C₁ + m₂ C₂  = 2 m₁ C₁    by (1)
 
Specific heat of the combined body
    = heat capacity / total mass
    = 2 m₁ C₁ / (m₁ + m₂)
    = 2 m₁ C₁ / [m₁ + m₁ C₁ / C₂]
    = 2 C₁ C₂ / [ C₁ + C₂ ]