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Question
Two blocks P and Q of different metals having their mass in the ratio 2 : 1 are given same amount of heat. Their temperature rises by same amount. Compare their specific heat capacities.
Solution
Specific heat capacity,
C = `"Amount of heat supplied"/"Mass × Rise in temperature"`
C = `"Q"/("m" xx Δ"t")`
Heat input and temperature increase are identical for blocks P and Q. Assume P has a mass of 2 m and Q a mass of m, with C1 and C2 being their specific heat capacities, respectively.
So C1 = `"Q"/(2"m" xx Δ"t")`
and C2 = `"Q"/("m" xx Δ"t")`
So C1 : C2 = `"Q"/(2"m" xx Δ"t") ÷ "Q"/("m" xx Δ"t")`
= `"Q"/(2"m" xx Δ"t") ÷ ("m" xx Δ"t")/"Q"`
C1 : C2 = `1/2`
= 1 : 2
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