Chapter 15.2, Problem 16SSC

Interpretation Introduction

Interpretation:

The mathematical formula used to calculate the amount of heat absorbed or released by a substance when its temperature changes is to be explained.

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 16SSC

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.

Explanation of Solution

Imagine $1kg$ of a substance undergoes a temperature change from 10 degree Celsius to 20 degree Celsius. It has a specific heat capacity of $2J/kg°C$.

The heat absorbed will be,

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

Here,

$\begin{array}{l}m=1kg\\ c=2J/kg°C\\ \Delta T=10°C-20°C\end{array}$

So,

$\begin{array}{l}Q=1kg\times \left(2J/kg°C\right)\times (10°C-20°C)\\ Q=1kg\times \left(2J/kg°C\right)\times (-10°C)\\ Q=-20J\end{array}$

This explains the use of the formula.

Conclusion

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

$\mathrm{Q}=m\times c\times \Delta \mathrm{T}$