Question

How much heat in joules and in calories, must be added to a $75gm$ iron block with specific heat of $0.449J\,g{{m}^{-1}}\,{}^{o}{{C}^{-1}}$ to increase its temperature from ${{25}^{o}}C$ to its melting temperature of ${{1535}^{o}}C$?

Answer 1

Hint: The specific heat is the heat required per gram to raise the temperature of a substance. The heat required to change the temperature of iron slab depends on the mass and change in temperature. We can substitute the corresponding values in the following relation to calculate heat. Joules and calories are different units used to express energy or heat.
Formulas used:
$H=mc\Delta T$

Complete answer:
The specific heat of a substance is the heat required to increase the temperature of a substance by $1{}^{o}C$ per unit mass. Therefore, it is given by-
$H=mc\Delta T$
Here, $H$ is the heat given to the substance
$m$ is the mass
$c$ is specific heat
$\Delta T$ is the change in temperature
Given, for an iron block, $m=75gm$, $c=0.449J\,g{{m}^{-1}}\,{}^{o}{{C}^{-1}}$, $\Delta T=1535-25=1510{}^{o}C$
We substitute given values in the above equation to get,
$\begin{align}
  & H=75\times 0.449\times 1510 \\
 & \Rightarrow H=50.85J \\
\end{align}$
Therefore, the heat required to increase the temperature of iron in joules is $50.85J$.
The relation between joules and calories is-
$1cal=4.2J$ - (1)
Using eq (1), we convert $50.85J$ into calories as-
$\begin{align}
  & x\,cal=\dfrac{50.85J}{4.2} \\
 & \Rightarrow x\,cal=12.11cal \\
\end{align}$
Therefore, the heat required in calories to change the temperature of iron slab is $12.11cal$.
Therefore, the heat required to change the temperature of iron slab to its melting temperature in joules is $50.85J$ and in calories is $12.11cal$.

Note:
To calculate the heat required to melt the iron slab, we will have to calculate its latent heat. To change the state of a substance, latent heat is used. The specific heat of a substance is constant, and is different for different substances. Specific heat can also be described as the heat capacity of a substance.