The specific heat of a substance varies with temperature t- C asc - 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

Heat 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 ...

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Standard XIII

Physics

Specific Heat Capacity

The specific ...

Question

The specific heat of a substance varies with temperature $t (^{\circ} C)$ as
$c = 0.20 + 0.14 t + 0.023 t^{2} (c a l / g m^{\circ} C)$ The heat required to raise the temperature of 2 gm of substance from $5^{\circ} C t o 15^{\circ} C$

24 calorie

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56 calorie

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82 calorie

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100 calorie

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Solution

The correct option is C 82 calorie
Heat required to raise the temperature of m gm of substance by dT is given as
$d Q = m c d T \Rightarrow Q = \int m c d T$
$∴$ To raise the temperature of 2 gm of substance from $5^{\circ} C t o 15^{\circ} C$
$Q = \int_{5}^{15} 2 \times (0.2 + 0.14 t + 0.023 t^{2}) d T = 2 \times {[0.2 t + \frac{0.14 t^{2}}{2} + \frac{0.023 t^{3}}{3}]}_{5}^{15} = 82 c a l o r i e$

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Similar questions

Q. The specific heat of a substance varies with temperature

t (^{\circ} C)

c = 0.20 + 0.14 t + 0.023 t^{2} (c a l / g m^{\circ} C)

The heat required to raise the temperature of 2 gm of substance from

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Q. The specific heat of a substance varies with temperature according to the function

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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

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

The specific heat of a substance varies with temperature $t (^{\circ} C)$ as
$c = 0.20 + 0.14 t + 0.023 t^{2} (c a l / g m^{\circ} C)$ The heat required to raise the temperature of 2 gm of substance from $5^{\circ} C t o 15^{\circ} C$