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Question
Two substances A and B have specific heats c and 2 c respectively. If A and B are given Q and 4Q amounts of heat respectively, the change in their temperatures is the same. If the mass of A is m, what is the mass of B?
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Solution
Let the mass of B = M.
Let the change in temperature be T for both the bodies, A and B.
The amount of heat in a body is given as
Q = m × c × Δ T
For body A,
Q = m × c × T
`=> "T" = "Q"/("mc")` ...(i)
For body B,
4Q = M × 2c × T
`=> "M" = (4"Q")/(2"c" xx "T")`
From (i), T = `Q/(mc)`
`=> "M" = (4Q)/(2c xx Q/(mc)) = 2m`
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