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  4. Given that the specific heat in cal/g is c=0.6 t 2, where t is the temperature on the celsius scale. If the temperature of 10 g of water is raised through 15° C, what is the amount of heat required?

Q. Given that the specific heat in $cal/g$ is $c=0.6\, t ^{2}$, where $t$ is the temperature on the celsius scale. If the temperature of $10\, g$ of water is raised through $15^{\circ} C$, what is the amount of heat required?

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Solution:

Given that $c=0.6\, t ^{2}$
We use
$d Q =m c d t$
$\int\limits_{0}^{Q} d Q =\int\limits_{0}^{15} 10 \times 0.6\, t^{2} d t$
$Q =6\left[\frac{t^{3}}{3}\right]_{0}^{15}=2(15)^{3}=6750\, cal$

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