Chapter 10, Problem 25QAP

Interpretation Introduction

(a)

Interpretation:

Convert 75.2 kcal to joules and kilojoules.

Concept Introduction:

A conversion factor is a numerical ratio which is used to show a measurement in one unit as another unit. It is always equal to 1.

Answer to Problem 25QAP

75.2 kcal = $\text{314}\text{.6368 kJ}$ and $\text{314636}\text{.8 J}$.

Explanation of Solution

The given conversion is: conversion of kilocalories to joules and kilojoules.

1 kilocalorie is equal to the 4184 joules and 4.184 kilojoules.

1 kcal = 4184 J and 1 kcal = 4.184 kJ

Thus, conversion factor is given by:

$\frac{\text{4184 J}}{\text{1 kcal}}\text{ and}\frac{\text{4}\text{.184 kJ}}{\text{1 kcal}}$

So,

$\text{75}\text{.2 kcal}$

$=\frac{\text{4}\text{.184 kJ}}{\text{1 kcal}}\times 75.2\text{ kcal=314}\text{.6368 kJ}$

$\text{75}\text{.2 kcal}$

$=\frac{\text{4184 J}}{\text{1 kcal}}\times \text{75}\text{.2 kcal=314636}\text{.8 J}$.

Interpretation Introduction

(b)

Interpretation:

Convert 75.2 cal to joules and kilojoules.

Concept Introduction:

A conversion factor is a numerical ratio which is used to show a measurement in one unit as another unit. It is always equal to 1.

Answer to Problem 25QAP

75.2 cal = $\text{314}\text{.6368 J}$ and $\text{0}\text{.3146368 kJ}$.

Explanation of Solution

The given conversion is: conversion of calories to joules and kilojoules.

1 calorie is equal to the 4.184 joules and 0.004184 kilojoules.

1 cal = 4.184 J and 1 cal = 0.004184 kJ

Thus, conversion factor is given by:

$\frac{\text{4}\text{.184 J}}{\text{1 cal}}\text{ and}\frac{\text{0}\text{.004184 kJ}}{\text{1 cal}}$

So,

$\text{75}\text{.2 cal}$

$=\frac{\text{4}\text{.184 J}}{\text{1 cal}}\times 75.2\text{ cal=314}\text{.6368 J}$

$\text{75}\text{.2 cal}$

$=\frac{\text{0}\text{.004184 kJ}}{\text{1 cal}}\times \text{75}\text{.2 cal=0}\text{.3146368 kJ}$.

Interpretation Introduction

(c)

Interpretation:

Convert $\text{1}\text{.41}\times {\text{10}}^3\text{ cal}$ to joules and kilojoules.

Concept Introduction:

A conversion factor is a numerical ratio which is used to show a measurement in one unit as another unit. It is always equal to 1.

Answer to Problem 25QAP

$\text{1}\text{.41}\times {\text{10}}^3\text{ cal}$ = $\text{5}\text{.899}\times {\text{10}}^3\text{ J}$ and $\text{0}\text{.005899}\times {10}^3\text{ kJ}$.

Explanation of Solution

The given conversion is: conversion of calories to joules and kilojoules.

1 calorie is equal to the 4.184 joules and 0.004184 kilojoules.

1 cal = 4.184 J and 1 cal = 0.004184 kJ

Thus, conversion factor is given by:

$\frac{\text{4}\text{.184 J}}{\text{1 cal}}\text{ and}\frac{\text{0}\text{.004184 kJ}}{\text{1 cal}}$

So,

$\text{1}\text{.41}\times {\text{10}}^3\text{ cal}$

$=\frac{\text{4}\text{.184 J}}{\text{1 cal}}\times \text{1}\text{.41}\times {\text{10}}^3\text{ cal=5}\text{.89944}\times {\text{10}}^3\text{ J}$

$\text{1}\text{.41}\times {\text{10}}^3\text{ cal}$

$=\frac{\text{0}\text{.004184 kJ}}{\text{1 cal}}\times 1.41\times {10}^3\text{ cal=0}\text{.005899}\times {10}^3\text{ kJ}$.

Interpretation Introduction

(d)

Interpretation:

Convert $\text{1}\text{.41}\times {\text{10}}^3\text{ kcal}$ to joules and kilojoules.

Concept Introduction:

A conversion factor is a numerical ratio which is used to show a measurement in one unit as another unit. It is always equal to 1.

Answer to Problem 25QAP

$\text{1}\text{.41}\times {\text{10}}^3\text{ cal}$ = $\text{5899}\text{.44}\times {\text{10}}^3\text{J}$ and $\text{5}\text{.89944}\times {\text{10}}^3\text{ kJ}$.

Explanation of Solution

The given conversion is: conversion of kilocalories to joules and kilojoules.

1 kilocalorie is equal to the 4184 joules and 4.184 kilojoules.

1 kcal = 4184 J and 1 kcal = 4.184 kJ

Thus, conversion factor is given by:

$\frac{\text{4184 J}}{\text{1 kcal}}\text{ and}\frac{\text{4}\text{.184 kJ}}{\text{1 kcal}}$

So,

$\text{1}\text{.41}\times {\text{10}}^3\text{ kcal}$

$=\frac{\text{4}\text{.184 kJ}}{\text{1 kcal}}\times \text{1}\text{.41}\times {\text{10}}^3\text{ kcal=5}\text{.89944}\times {\text{10}}^3\text{ kJ}$

$\text{1}\text{.41}\times {\text{10}}^3\text{ kcal}$

$=\frac{\text{4184 J}}{\text{1 kcal}}\times \text{1}\text{.41}\times {\text{10}}^3\text{ kcal=5899}\text{.44}\times {\text{10}}^3\text{ J}$.