Chapter 7, Problem 57E

Interpretation Introduction

Interpretation: The specific heat capacity of the metal to be calculated.

Concept Introduction: The heat capacity C is defined as the ratio of heat absorbed to the temperature change. It can be given by,

                           $\text{C = }\frac{\text{heat absorbed}}{\text{temperature change}}$

• Require heat of one gram of substance raise to its temperature by one degree Celsius is called specific heat capacity.

                       $\text{Specific heat capacity = }\frac{\text{Absorbed heat }\left(\text{J}\right)}{\text{Temperature change×mass of}\text{substance }\left(\text{g}\right)}\mathrm{......}\left(\text{1}\right)$

For in above equation heat is:

$\begin{array}{l}\text{q = S×M×T}\mathrm{......}\left(\text{2}\right)\hfill \\ \text{q is heat }\left(\text{J}\right)\hfill \\ \text{M is mass of sample }\left(\text{g}\right)\hfill \\ \text{S is specific heat capacity }\left(\text{J/°C×g}\right)\hfill \\ \text{T istemperature change }\left({}^{\text{o}}\text{C}\right)\hfill \end{array}$

For the process no heat loss to the surroundings means then the heat is

$\text{q }\left(\text{absorbed}\right)\text{ =}\text{-q }\left(\text{released}\right)\mathrm{......}\left(\text{3}\right)$