Chapter 14, Problem 22P

To determine

Section 1:

The heat gained.

Answer to Problem 22P

Solution:

The heat gained is $47.26\text{ kcal}$.

Explanation of Solution

Given info:

The mass of sample cookies is $\text{10 g}$, the mass of aluminum container is $0.615\text{ kg}$, the mass of water is $\text{2 kg}$, the mass of aluminum calorimeter cup is $\text{0}\text{.524 kg}$, the initial temperature is $15°\text{C}$ and the final temperature is $\text{36 }°\text{C}$.

The principle of calorimetric is written as,

$\text{Heat lost}=\text{Heat gained}$

The heat gained is calculated as,

$\begin{array}{c}\text{Heat gained}=+\left(m_{\text{Al}}{c}_{\text{Al}}\left(T_{\text{f}}-T_{\text{i}}\right)+m_{\text{w}}{c}_{\text{w}}\left(T_{\text{f}}-T_{\text{i}}\right)+m_{\text{C}}{c}_{\text{Al}}\left(T_{\text{f}}-T_{\text{i}}\right)\right)\\ =\left(T_{\text{f}}-T_{\text{i}}\right)\left(m_{\text{Al}}{c}_{\text{Al}}+m_{\text{w}}{c}_{\text{w}}+m_{\text{C}}{c}_{\text{Al}}\right)\end{array}$

$m_{\text{Al}}$ is the mass of aluminum container.

• $m_{\text{w}}$ is the mass of water.

• $m_{\text{C}}$ is the mass of calorimeter.

• $c_{\text{Al}}$ is the specific heat capacity of aluminum.

• $c_{\text{w}}$ is the specific heat capacity of water.

• $T_{\text{f}}$ is the final temperature.

• $T_{\text{i}}$ is the initial temperature.

Substitute $\text{0}\text{.615 kg}$

for $m_{\text{Al}}$, $\text{2 kg}$ for $m_{\text{w}}$, $0.524\text{kg}$ for $m_{\text{C}}$

$0.22\text{kcal}/\text{kg }°\text{C}$ for $c_{\text{Al}}$, $\text{1 }\text{kcal}/\text{kg }°\text{C}$ for $c_{\text{w}}$, $15°\text{C}$ for $T_{\text{i}}$ and $\text{36 }°\text{C}$ for $T_{\text{f}}$ in above equation to find heat gained.

$\begin{array}{c}\text{Heat gained}=\left(\text{36 }°\text{C}-15°\text{C}\right)\left\{\begin{array}{l}\left(\text{0}\text{.615 kg}\right)\left(0.22\text{kcal}/\text{kg }°\text{C}\right)\\ +\left(\text{2 kg}\right)\left(\text{1 }\text{kcal}/\text{kg }°\text{C}\right)\\ +\left(\text{0}\text{.524 kg}\right)\left(0.22\text{kcal}/\text{kg }°\text{C}\right)\end{array}\right\}\\ =47.26\text{ kcal}\end{array}$

To determine

Section 2:

The energy content of $\text{100 g}$ Karen’s fudge cookies.

Answer to Problem 22P

Solution:

The energy content of $\text{100 g}$ Karen’s fudge cookies is $\underset{\_}{472.6\text{kcal}}$.

Explanation of Solution

Given info:

The mass of sample cookies is $\text{10 g}$, the mass of aluminum container is $0.615\text{ kg}$, the mass of water is $\text{2 kg}$, the mass of aluminum calorimeter cup is $\text{0}\text{.524 kg}$, the initial temperature is $15°\text{C}$ and the final temperature is $\text{36 }°\text{C}$.

The heat gained is nothing but the amount of energy that was liberated from the $\text{10 g}$ sample.

The energy liberated from the $\text{100 g}$ is calculated as,

$\begin{array}{c}E=\text{Heat gained}\times \frac{\text{100 g}}{10\text{ g}}\\ =47.26\text{ kcal}\times \frac{\text{100 g}}{10\text{ g}}\\ =472.6\text{ kcal}\end{array}$