Chapter U5, Problem C19.2RE

(a)

Interpretation Introduction

Interpretation: The amount of energy in calories that can be transformed from the combustion of one peanut to be calculated.

Concept Introduction: Thermodynamics is the analysis of heat transfer. Heat transfer direction is always from a hotter substance to colder one.

Answer to Problem C19.2RE

Amount of energy that can be transformed from the combustion of one peanut is 1000cal.

Explanation of Solution

Given mass of water (m) = 100g

Temperature change $\left(\Delta \text{T}\right)=10°\text{C}$

Specific heat of water is $\text{1}\text{cal}/\text{g}\cdot °\text{C}$

The equation of heat is as follows:

  $\text{H=mCΔT}$

Here H is heat, m is mass, C is specific heat and T is temperature.

Put the values in above equation is as follows:

  $\begin{array}{c}\text{H=100}\cancel{\text{g}}\times \text{1}\frac{\text{cal}}{\cancel{\text{g}}\text{×}\cancel{°\text{C}}}\times 10\cancel{\text{°C}}\\ \text{H=1000}\text{cal}\end{array}$

Thus, amount of energy that can be transformed from the combustion of one peanut is 1000cal.

(b)

Interpretation Introduction

Interpretation: The amount of calories per gram of peanut to be calculated.

Concept Introduction: Thermodynamics is the analysis of heat transfer. Heat transfer direction is always from a hotter substance to colder one.

Answer to Problem C19.2RE

The amount of calories per gram of peanut is $392.15\text{6}\text{cal}/\text{g}$ .

Explanation of Solution

Given initial mass of peanut = 3.75g

Final mass of peanut = 1.2 g

Thus

  $\begin{array}{c}\text{ burned mass }=\text{3}.\text{75g}-1.2g\\ =2.55\text{g}\end{array}$

  $\begin{array}{c}\text{Energy per gram }\left(\text{e}\right)=\frac{1000\text{cal}}{2.55\text{g}}\\ =392.15\text{6}\text{cal}/\text{g}\end{array}$

Thus the amount of calories per gram of peanut is $392.15\text{6}\text{cal}/\text{g}$ .

(c)

Interpretation Introduction

Interpretation: The amount of food calories in the bag to be calculated.

Concept Introduction: Thermodynamics is the analysis of heat transfer. Heat transfer direction is always from a hotter substance to colder one.

Answer to Problem C19.2RE

Amount of food calories in the bag is 196078 cal.

Explanation of Solution

Given mass of peanut (M) =500 g

  $\begin{array}{c}\text{Total energy }\left(\text{E}\right)\text{ = e×M}\\ \text{= 392}\text{.156}\frac{\text{cal}}{\cancel{\text{g}}}\text{×500}\cancel{\text{g}}\\ \text{=196078cal}\end{array}$

Thus, amount of food calories in the bag is 196078 cal.