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Question

Question: Two bodies of specific heats S<sub>1</sub> and S<sub>2</sub> having same heat capacities are combine...

Two bodies of specific heats S1 and S2 having same heat capacities are combined to form a single composite body. Specific heat of composite body is –

A

S1 + S2

B

S1+S22\frac{S_{1} + S_{2}}{2}

C

2S1S2S1+S2\frac{2S_{1}S_{2}}{S_{1} + S_{2}}

D

1S1\frac{1}{S_{1}} + 1S2\frac{1}{S_{2}}

Answer

2S1S2S1+S2\frac{2S_{1}S_{2}}{S_{1} + S_{2}}

Explanation

Solution

m1 s1 = m2 s2 …...(1)

m1 s1 + m2 s2 = (m1 + m2) s ….(2)

s = m1s1+m2s2m1+m2\frac{m_{1}s_{1} + m_{2}s_{2}}{m_{1} + m_{2}} = 2m1s1m1+m2\frac{2m_{1}s_{1}}{m_{1} + m_{2}} (\ m1s1 = m2s2 )

= 2m1s1m1+m1s1s2\frac{2m_{1}s_{1}}{m_{1} + \frac{m_{1}s_{1}}{s_{2}}} = 2s1s2s1+s2\frac{2s_{1}s_{2}}{s_{1} + s_{2}}