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The specific heat of a substance varies ...

The specific heat of a substance varies as `(3 theta^(2) + theta) xx 10^(3) cal g^(-10) C^(-1)`. What is the amount of heat required to rise the temperature of `1 kg` of substance frm `10^@C` to `20^@ C` ?

Text Solution

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For small change in temperature `d theta`, heat required, `dQ = mSd theta`.
`:. Q = underset(theta_(1))overset(theta_(2))int mSd theta`
`:. Q = underset(10) overset(20) int 1000(3 theta^(2) +theta) xx 10^(-3) d theta = |theta^(3)+ theta^(2)/(2)|_(10)^(20)`
=`(20^(3) +(20^(2))/(2)) -(10^(3)+(10^(2))/(2)) = 8200 -1050 = 7150 cal`.
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