Question

Solid magnesium has a specific heat of $1.01\,Jg{{m}^{-1}}{}^{o}{{C}^{-1}}$. How much heat is given off by a $20gm$ sample of magnesium when it cools from $70{}^{o}C$ to $50{}^{o}C$?

Answer 1

Hint: When the temperature of a substance increases heat is absorbed by it, whereas when it decreases, heat is released. Specific heat of a substance is the heat required to increase the unit temperature of unit mass. Therefore, by substituting values in the relation we can calculate the heat released.
Formulas used:
$c=\dfrac{Q}{m\Delta T}$

Complete step-by-step solution:
Specific heat is defined as the heat required to raise the temperature of $1gm$of a substance by $1{}^{o}C$. Its SI unit is $Jk{{g}^{-1}}{{K}^{-1}}$. It is given as-
$c=\dfrac{Q}{m\Delta T}$-------- (1)
Here, $c$ is the specific heat
$Q$ is the heat required
$m$ is the mass of substance
$\Delta T$ is change in temperature
Given, for solid magnesium, $c=1.01\,Jg{{m}^{-1}}{}^{o}{{C}^{-1}}$, $m=20gm$
$\begin{align}
  & \Delta T=(70-50){}^{o}C \\
 & \Rightarrow \Delta T=20{}^{o}C \\
\end{align}$
From eq (1), we have,
$Q=mc\Delta T$
We substitute given values in the above equation to get,
$\begin{align}
  & Q=20\times 1.01\times 20 \\
 & \Rightarrow Q=4,04J \\
\end{align}$
Therefore, the heat required to change the temperature of magnesium by $20{}^{o}C$ is $4.04J$.

Additional Information: At constant temperature, the heat can change the state of a substance. The heat absorbed or released at a constant temperature to change the state of a substance is called latent heat. The heat required to change a liquid substance into vapor form is called the latent heat of vaporization, heat required to change a liquid into a solid form is called the latent heat of fusion.

Note: To change the temperature of one mole of a substance, molar specific heat is used. At constant volume, heat changes the temperature, whereas, at a constant temperature, heat changes the volume of a substance. The specific heat is a constant and depends on the substance and temperature; it is different for different substances and highest for water at $4.186Jg{{m}^{-1}}{}^{o}C$.