Chapter 9, Problem 9.15PAE

9.15 Carry out the following conversions of energy units:

(a) 14.3 Btu Into calories, (b) $1.4\times \text{1}{0}^5$ cal into joules, (c) 31.6 mJ into Btu

Interpretation Introduction

(a) Interpretation:

The number of calories that are equal to $\text{14}\text{.3 Btu}$ of energy

Explanation of Solution

We know that

$1Btu=\text{ 252}\text{.055 }Calories$

Thus, we have two possible conversion factors as follows:

$\frac{1Btu}{\text{252}\text{.055 }Calories}$ and $\frac{\text{252}\text{.055 }Calories}{1Btu}$

Now, Amount of Energy in Btu= $14.3Btu$

Using the above conversion factor, the amount of energy in Calories is given as follows:

Amount of Energy $=14.3Btu\times \frac{\text{252}\text{.055 }Calories}{1Btu}$

Thus, the amount of Energy $=\text{ 3604}.4Calories$

Thus, $14.3Btuofenergy=\text{ 3604}.4Caloriesofenergy$

Interpretation Introduction

(b) Interpretation:

The value in Joules that is equal to $\text{1}{\text{.4 × 10}}^{\text{5}}\text{ Cal}$ of energy

Explanation of Solution

We know that $\text{1 Calorie = 4}\text{.1868 Joules}$

Thus, we have two possible conversion factors as follows:

$\frac{1Calorie}{\text{4}\text{.1868 }Joules}$ and $\frac{\text{4}\text{.1868 }Joules}{1Calorie}$

Now, Amount of Energy in Calorie = $1.4\times {10}^{5}Cal$

Using the above conversion factor, the amount of energy in Calories is given as follows:

Amount of Energy $=1.4\times {10}^{5}Cal\times \frac{\text{4}\text{.1868 }Joules}{1Calorie}$

Thus, the amount of Energy $=\text{ 586152 }Joules$

Thus, $1.4\times {10}^{5}Calofenergy=\text{586152 }Joulesofenergy$

Interpretation Introduction

(c) Interpretation:

The value in Btu equal to $\text{31}\text{.6 mJ}$ of energy

Explanation of Solution

We know that

$1mJ=\text{ 0}\text{.00000095 }Btu$

Thus, we have two possible conversion factors as follows:

$\frac{1mJ}{\text{0}\text{.00000095 }Btu}$ and $\frac{\text{0}\text{.00000095 }Btu}{1mJ}$

Now, Amount of Energy in Btu = $\text{31}\text{.6 }mJ$

Using the above conversion factor, the amount of energy in Calories is given as follows:

Amount of Energy $=\text{ 31}\text{.6 }mJ\times \frac{\text{0}\text{.00000095 }Btu}{1mJ}$

Thus, the amount of Energy $=\text{ 0}\text{.00002951 }Btu$

Thus, $1\text{31}\text{.6 }mJofenergy=\text{0}\text{.00002951 }Btuofenergy$

Conclusion

Hence, the required conversions of energy units are determined.