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Question

# The specific heat of a substance varies with temperature t(∘C) as c=0.20+0.14 t+0.023 t2 (cal/gm∘ C) The heat required to raise the temperature of 2 gm of substance from 5∘ C to 15∘ C

A
24 calorie
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B
56 calorie
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C
82 calorie
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D
100 calorie
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Solution

## The correct option is C 82 calorieHeat required to raise the temperature of m gm of substance by dT is given as dQ=mc dT⇒Q=∫mc dT ∴ To raise the temperature of 2 gm of substance from 5∘ C to 15∘ C Q=∫1552×(0.2+0.14t+0.023t2)dT=2×[0.2t+0.14t22+0.023 t33]155=82 calorie

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