Chapter 15.2, Problem 19SSC

Interpretation Introduction

Interpretation:

The need for specific heat capacity in calculating the amount of heat absorbed or released by a substance when its temperature changes is to be highlighted.

Concept introduction:

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.

Answer to Problem 19SSC

The mathematical formula to calculate the heat absorbed or released by a substance when the temperature changes is,

$Q=m\times c\times \Delta T$

Where,

$Q$ is the heat released or absorbed,

$m$ is the mass of the substance,

$c$ is the specific heat of the substance,

$\Delta T$ is the difference between the initial and the final temperatures.

The specific heat capacity is a constant. By knowing the value of this fixed constant, the amount of heat produced or amount for an unknown mass of the substance can be directly calculated.

Explanation of Solution

Let say a 1kg of a substance melts by absorbing Q amount of heat and a temperature change of T.

Now, to determine how much heat would be required to melt 20kg of this substance, can only be determined by actually experimenting with it or by using the mathematical formula of heat capacity. In this formula, only variable is the temperature change, mass and specific heat capacity are fixed parameters. This way the amount of heat needed can be calculated easily.

Conclusion

The mathematical formula to calculate the heat absorbed or released by a substance when its temperature changes is,

$Q=m\times c\times \Delta T$

The specific heat capacity is a property of the substance. It is a constant and can be directly used in the above formula to calculate heat absorbed or released by different masses of the substance.