Question

Molten iron is extremely hot, averaging about ${{1500}^{o}}C$ . The specific heat of iron is $0.46J{{\left( g{{\ }^{o}}C \right)}^{-1}}$ . How much heat is released to the atmosphere when $1kg$ molten iron cools to room temperature $\left( {{25}^{o}}C \right)$ ?

Answer 1

We know that the specific heat is the amount of heat required to change the temperature of 1kg of mass of a substance by ${{1}^{o}}C$ . For the given question, to calculate heat released in the given process we will use the quantitative relation between heat transfer, mass, specific heat and change in temperature and will substitute the given values to get the required result.
$Q=mc\Delta T\ \ \ ...(1)$
Where, Q is the heat transfer, m is the mass of the substance, $\Delta T$ is the change in temperature and c is the specific heat of the substance.

Complete Step By Step Answer:
As per question, the given data is as follows:
Specific heat of iron $=0.46J{{\left( g{{\ }^{o}}C \right)}^{-1}}$
Mass of iron $=1kg\Rightarrow 1000g$
Initial temperature ${{T}_{1}}={{1500}^{o}}C$
Final temperature ${{T}_{2}}={{25}^{o}}C$
Now, as per equation (1), the heat transfer on the given transformation is as follows:
$Q=mc\Delta T$
$\Delta T$ is the change in temperature that means it is the difference between final temperature and initial temperature. Thus, the expression can also be expressed as follows:
$\Rightarrow Q=mc({{T}_{2}}-{{T}_{1}})\ \ \ \ ...(2)$
Substituting given values in equation (2), the heat transfer for the given process is as follows:
$\Rightarrow Q=1000\times 0.46\times (25-1500)$
$\Rightarrow Q=-678500J$
As $1kJ=1000J$ , so in terms of kilojoule, the heat transfer for the process will be as follows:
$\Rightarrow Q=-678.5J$
The negative sign here indicates that the cooling of molten iron is an exothermic process that means the heat is released when molten iron cools to room temperature.
Thus, we can conclude that the heat released in the given process is $678.5J$ .

Note:
Remember that unlike total heat capacity, the specific heat capacity is independent of volume or mass. The values of specific heat are dependent on the properties and phase of a given substance and can only be empirically measured.