Chapter 13, Problem 1P

To determine

Find the amount of natural gas needed to burn to heat twenty gallons of water.

Answer to Problem 1P

The amount of natural gas needed to burn to heat twenty gallons of water is $0.1668{\text{ft}}^3$ of natural gas.

Explanation of Solution

Calculation:

The volume of used natural gas depends upon the rise of temperature and the efficiency of the heater. Typically, the heating value of the natural gas ranges from $950\frac{\text{Btu}}{{\text{ft}}^{\text{3}}}$ to $1150\frac{\text{Btu}}{{\text{ft}}^{\text{3}}}$.

Therefore, assume that the heating value of natural gas is $1000\frac{\text{Btu}}{{\text{ft}}^{\text{3}}}$, and the efficiency for rise of every degree of temperature is $100\%$.

Convert the twenty gallons of water into pound.

$\left(20\text{gallons of water}\right)\left(\frac{8.34\text{pounds}}{1\text{gallon of water}}\right)=166.8\text{pounds}$.

The specific heat capacity of water is $1\frac{\text{Btu}}{\text{pound}\cdot °\text{F}}$. Convert the values to Fahrenheit in order to calculate the heat for rise of every degree of temperature.

$\left(166.8\text{pounds}\right)\left(\frac{\text{1}\text{Btu}}{\text{pound}\cdot °\text{F}}\right)\left(1°\text{F}\right)=166.8\text{Btu}$

Hence, the volume of natural gas used is,

$\left(166.8\text{Btu}\right)\left(\frac{1{\text{ft}}^3\text{of natural gas}}{\text{1000}\text{Btu}}\right)=0.1668{\text{ft}}^3\text{of natural gas}$

Therefore, the amount of natural gas needed to burn to heat twenty gallons of water is $0.1668{\text{ft}}^3$ of natural gas.

Conclusion:

Thus, the amount of natural gas needed to burn to heat twenty gallons of water is $0.1668{\text{ft}}^3$ of natural gas.