Question

Two bodies of specific heats S1 and S2 having the same heat capacities are combined to form a single composite body. What is the specific heat of the composite body?​

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}♨`

Heat capacity of body 1 :

`\qquad \sf  \dashrightarrow \:m_1s_1`

Heat capacity of body 2 :

`\qquad \sf  \dashrightarrow \:m_2s_2`

it's given that, the the head capacities of both the objects are equal. I.e

`\qquad \sf  \dashrightarrow \:m_1s_1 = m_2s_2`

`\qquad \sf  \dashrightarrow \:m_1 = (m_2s_2)/(s_1)`

Now, consider specific heat of composite body be s'

According to given relation :

`\qquad \sf  \dashrightarrow \:(m_1 + m_2) s' = m_1s_1 + m_2s_2`

`\qquad \sf  \dashrightarrow \:s' = ( m_1s_1 + m_2s_2)/(m_1 + m_2)`

`\qquad \sf  \dashrightarrow \:s' = ( m_2s_2+ m_2s_2)/( (m_2s_2)/(s_1) + m_2 )`

[ since,
`m_2s_2 = m_1s_1` ]

`\qquad \sf  \dashrightarrow \:s' = ( 2m_2s_2)/( m_2((s_2)/(s_1) + 1))`

`\qquad \sf  \dashrightarrow \:s' = \frac{ 2 \cancel{m_2}s_2}{ \cancel{m_2}((s_2)/(s_1) + 1)}`

`\qquad \sf  \dashrightarrow \:s' = ( 2 s_2)/( ((s_2 + s_1)/(s_1) ))`

`\qquad \sf  \dashrightarrow \: s' = (2s_1s_2)/(s_1 + s_2)`

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