Chapter SH, Problem 5.3APP

To determine

To calculate: Energy needed to heat sand.

Answer to Problem 5.3APP

Energy needed to heat sand is $\underset{\_}{13280\text{ J}}$ .

Explanation of Solution

Given:

Specific heat = $\text{664 J/}\left(\text{kg}\cdot °\text{C}\right)$

Initial temperature = $30°\text{C}$

Final temperature = $\text{50}°\text{}\text{C}$

Mass = $1.0\text{ kg}$

Formula used:

Change in thermal energy is given by,

  $Q=m\left(T_{\text{f}}-T_{\text{i}}\right)C$

where $m$ is mass, $T_{\text{f}}$ is final temperature, $T_{\text{i}}$ is initial temperature and C is specific heat.

Calculation:

Energy needed to heat sand is calculated as:

  $\begin{array}{l}Q=m\left(T_{\text{f}}-T_{\text{i}}\right)C\\ Q=\left(1\text{ kg}\right)\left(50°\text{C}-30°\text{C}\right)\left(\text{664 J/}\left(\text{kg}\cdot °\text{C}\right)\right)\\ Q=\left(1\text{ kg}\right)\left(20°\text{C}\right)\left(\text{664 J/}\left(\text{kg}\cdot °\text{C}\right)\right)\\ Q=13280\text{ J}\end{array}$

Conclusion:

Energy needed to heat sand is $\underset{\_}{13280\text{ J}}$ .