Chapter 15.2, Problem 22SSC

Interpretation Introduction

Interpretation:

A procedure to determine the specific heat of a 45g piece of metal is to be described.

Concept introduction:

Heat capacity:The heat absorbed or released by a substance is dependent on three factors:

1. The mass of the substance.
2. The nature of the substance, its specific heat capacity.
3. The change in temperature of the substance.

The unit of heat is Joules (J), specific heat capacity is J/(kg degree Celsius), and that of mass is kg.

Calorimeter: A device used to measure the amount of heat exchanged between an unknown substance and fixed amount of water present in it.

Answer to Problem 22SSC

Take a calorimeter with a fixed quantity of water at temperature $T_i$.

Drop the 45g metal at room temperature, t, into the calorimeter.

Record the change in temperature of the calorimeter when the metal comes in contact with the water. Let say the final temperature of water becomes $T_f$.

Since, the heat exchange is happening in an isolated system,

$\begin{array}{l}{Q}_m=-Q_{water}\\ c_m\times 45g\times \left(t-T_f\right)=-c_{water}\times m_{water}\times \left(T_i-T_f\right)\\ c_m=\frac{-c_{water}\times m_{water}\times \left(T_i-T_f\right)}{45g\times \left(t-T_f\right)}\end{array}$

By substituting the recorded values of temperatures and mass of water, the specific heat of metal can be calculated.

Explanation of Solution

The experiment uses the fact that in an isolated system, the amount of heat released or absorbed is zero. The metal and water exchange heat inside the calorimeter and attain equilibrium. At equilibrium, the final temperature of both metal and water is the same. The known parameters like the amount of water, specific heat of water, room temperature, initial temperature of water, and final temperature can be substituted in the heat exchange formula to get the specific heat of the metal.

Conclusion

The specific heat of the 45g piece of metal can be calculated using the formula:

$c_m=\frac{-c_{water}\times m_{water}\times \left(T_i-T_f\right)}{45g\times \left(t-T_f\right)}$