Chapter 10, Problem 73AP

If 10. J of heat is applied to 5.0-g samples of each of the sub stances listed in Table 10.1, which substance’s temperature will increase the most? Which substance’s temperature wilt increase the least?

Interpretation Introduction

Interpretation:

The substances which have the most and the least increase in temperature listed in the table should be determined.

Concept Introduction:

Energy is the ability to do work or produce heat. The specific heat capacity is the amount of heat per unit mass needed to raise the temperature by 1⁰ C.

$\begin{array}{l}\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}\\ \text{w}\text{h}\text{e}\text{r}\text{e},\\ \text{Q}=\text{e}\text{n}\text{e}\text{r}\text{g}\text{y}\text{o}\text{r}\text{h}\text{e}\text{a}\text{t}\text{a}\text{p}\text{p}\text{l}\text{i}\text{e}\text{d}\\ \text{m}=\text{m}\text{a}\text{s}\text{s}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{u}\text{b}\text{s}\text{t}\text{a}\text{n}\text{c}\text{e}\\ \text{D}\text{T}=\text{c}\text{h}\text{a}\text{n}\text{g}\text{e}\text{i}\text{n}\text{t}\text{e}\text{m}\text{p}\text{e}\text{r}\text{a}\text{t}\text{u}\text{r}\text{e}\\ \text{s}=\text{s}\text{p}\text{e}\text{c}\text{i}\text{f}\text{i}\text{c}\text{h}\text{e}\text{a}\text{t}\text{c}\text{a}\text{p}\text{a}\text{c}\text{i}\text{t}\text{y}\text{o}\text{f}\text{s}\text{u}\text{b}\text{s}\text{t}\text{a}\text{n}\text{c}\text{e}\end{array}$.

Answer to Problem 73AP

Gold has highest increase in temperature and water(liquid) has the least increase in temperature.

Explanation of Solution

It is given that the mass of each substance is 5.0 g and energy is 10J. Specific heat capacity of each substance is also given in the table. Substituting these values in the formula above, we can calculate the change in temperature for each substance.

$\text{Δ}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}$

$\begin{array}{l}\text{F}\text{o}\text{r}\text{w}\text{a}\text{t}\text{e}\text{r}(\text{l}\text{i}\text{q}\text{u}\text{i}\text{d}),\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 4.184\text{J}/{\text{g}}^{\text{o}}\text{C}}=0.49^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{w}\text{a}\text{t}\text{e}\text{r}(\text{i}\text{c}\text{e}),\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 2.03\text{J}/{\text{g}}^{\text{o}}\text{C}}=0.98^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{w}\text{a}\text{t}\text{e}\text{r}(\text{s}\text{t}\text{e}\text{a}\text{m}),\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 2.0\text{J}/{\text{g}}^{\text{o}}\text{C}}=1^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{A}\text{l}\text{u}\text{m}\text{i}\text{n}\text{u}\text{m},\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 0.89\text{J}/{\text{g}}^{\text{o}}\text{C}}=2.2^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{I}\text{r}\text{o}\text{n},\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 0.45\text{J}/{\text{g}}^{\text{o}}\text{C}}=4.4^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{m}\text{e}\text{r}\text{c}\text{u}\text{r}\text{y},\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 0.14\text{J}/{\text{g}}^{\text{o}}\text{C}}=14^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{c}\text{a}\text{r}\text{b}\text{o}\text{n},\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 0.71\text{J}/{\text{g}}^{\text{o}}\text{C}}=2.8^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{s}\text{i}\text{l}\text{v}\text{e}\text{r},\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 0.24\text{J}/{\text{g}}^{\text{o}}\text{C}}=8.3^{\text{o}}\text{C}\\ \text{F}\text{o}\text{r}\text{g}\text{o}\text{l}\text{d},\text{D}\text{T}=\frac{\text{Q}}{\text{m}\times \text{s}}=\frac{10\text{J}}{5.0\text{g}\times 0.13\text{J}/{\text{g}}^{\text{o}}\text{C}}=15^{\text{o}}\text{C}\end{array}$

From the above calculations it is clearly shown that Gold has highest increase in temperature and water(liquid) has the least increase in temperature.

Conclusion

Therefore, Gold has most increase in temperature and water(liquid) has the least increase in temperature.