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The specific heat of a substance varies ...

The specific heat of a substance varies as `(3t^(2) + t) xx 10^(-3)` cal/`g^(0)`C. What is the amount of heat required to raise the temperature of 1 kg of substance from `10^(0)C " to " 20^(0)`C ?

Text Solution

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For small change in temperature dt, heat required,
dQ = msdt `therefore Q = int_(4)^(2) `msdt
Given, m = 1000 g, s = `(3t^(2) + t)`
`therefore Q = int_(10)^(20) 1000 (3t^(2) + t) xx 10^(-3) dt `
`= |t^(3) + (t^(2))/(2) |_(10)^(20) = (20^(3) + (20^(2))/(2) ) - (10^(3) + (10^(2))/(2) ) = 8200 - 1050` = 7150 cal
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