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# Describe a method to determine the specific heat capacity of a solid, like a piece of copper.

Last updated date: 06th Sep 2024
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Hint: The heat capacity of any substance is measured by using the principle of calorimetry. In this the substance is made to exchange the heat with another substance of known heat capacity inside an insulated container. Then equating the heat rejected by the substance with the heat absorbed by the substance, we get the required heat capacity of the substance.

Complete step-by-step solution
We know that the specific heat capacity of a substance is equal to the heat absorbed or rejected by the unit mass of the substance per degree Celsius temperature.
For measuring the heat capacity of a solid, we use a calorimeter. Let us assume the specific heat capacity of the substance as $C$ . Firstly, the mass of the given solid is noted, say $m$ . Then, it is heated by using a heater to a particular temperature $T$ . Then some particular mass of water, say ${m_W}$ , is taken in an insulated container and its temperature is recorded, say ${T_W}$ . Then the solid is dropped inside the water contained in the container. The solid is well stirred with the water so that they both achieve a particular highest temperature $T'$ which is recorded.
Now, from the theorem of conservation of energy, the heat lost by the solid must be equal to the heat gained by water. So we can have the following equation
$mC\left( {T - T'} \right) = {m_W}s\left( {T' - {T_W}} \right)$ ( $s$ is the specific heat capacity of water)
$\Rightarrow C = \dfrac{{{m_W}s}}{m}\dfrac{{\left( {T' - {T_W}} \right)}}{{\left( {T - T'} \right)}}$
From this equation, the heat capacity of the given solid is determined.

Note
The container used in the experiment is assumed to be having zero heat capacity, so that the heat absorbed by the container can be neglected. Also, dropping off the solid inside water must be gentle so as to ensure that there is no splashing of the water outside the container.