Question

Two bodies of specific heat capacities $S_{1}$ and $S_{2}$ have the same heat capacities. They are combined to form a single composite body. The specific heat capacity of the composite body is

• A. $S_{1}+S_{2}$
• B. $\frac{S_{1} + S_{2}}{2}$
• C. $\frac{2 S_{1} S_{2}}{S_{1} + S_{2}}$
• D. $\frac{1}{S_{1}}+\frac{1}{S_{2}}$

Answer 1

Answer: (C)

Given, $m_{1}S_{1}=m_{2}S_{2}$
$m_{1}S_{1}+m_{2}S_{2}=\left(m_{1} + m_{2}\right)S$
$S=\frac{m_{1} S_{1} + m_{2} S_{2}}{m_{1} + m_{2}}=\frac{2 m_{1} S_{1}}{m_{1} + m_{2}} \, \left(\therefore m_{1} S_{1} = m_{2} S_{2}\right)$
$=\frac{2 m_{1} S_{1}}{m_{1} + \frac{m_{1} S_{1}}{S_{2}}}=\frac{2 S_{1} S_{2}}{S_{1} + S_{2}}$