Chapter 10, Problem 54A

Interpretation Introduction

Interpretation: The substance whose temperature will increase the most and the substances whose temperature will increase the least needs to be determined if $\text{10}\text{.0}\text{J}$ of heat is added to $\text{5}\text{.0}\text{g}$ samples of each substances listed in the table given below.

  

Concept introduction: Specific heat of capacity can be defined as the amount of heat added to a substance to raise the temperature by one degree.

Answer to Problem 54A

The temperature of gold will increase the most and the temperature of liquid water will increase the least.

Explanation of Solution

The amount of heat added to $\text{5}\text{.0}\text{g}$ of the each sample is $\text{10}\text{.0}\text{J}$ .

  $\begin{array}{c}Q=s\times m\times \Delta T\\ 10.0\text{J}=s\times 5.0\text{g}\times \Delta T\\ \Delta T=\frac{\text{5}\text{J/g}}{\text{s}}\end{array}$

The change in temperature ( $\Delta T$ ) depends on the specific heat capacity of the given substances as:

From the above relation, the substance having smaller value of specific heat capacity is gold. Therefore, the temperature of gold will increase the most. The substance having larger value of specific heat capacity is liquid water. Therefore, the temperature of gold will increase the least.

Conclusion

The equation for heat is as follows:

  $\begin{array}{l}Q=s\times m\times \Delta T\\ \Delta T=\frac{Q}{s\times m}\\ \Delta T\propto \frac{1}{s}\mathrm{......}\left(1\right)\end{array}$

Where, Q is the amount of heat, m is the mass of substance, s is the specific heat capacity and $\Delta T$ is the temperature change.

From relation (1), there is an inverse relation between temperature change value and the specific heat capacity of the substances.