Question

The specific heat of a substance varies with temperature $t{(}^{\circ }C)$ as $c=0.20+0.14t+0.023t^2\left(cal/g^{\circ }C\right)$. The heat required to raise the temperature of $2g$ of substance from $5^{\circ }C$ to ${15}^{\circ }C$ will be

• A. $24cal$
• B. $56cal$
• C. $82cal$
• D. $100cal$

Answer 1

The correct option is C $82cal$

Let heat required be Q
Also temperature is denoted by t, mass of gas=m=2g
Then, $dQ=m\times c\times dt=2(0.20+0.14t+0.023t^2)dt$
$\Rightarrow Q=0.4\Delta t+0.14\Delta t^2+\frac{0.046}{3}\Delta t^3=4+28+50=82cal$