# In a large building, oil is used in a steam boiler heating system. The combustion of 1.0 pound of...

## Question:

In a large building, oil is used in a steam boiler heating system. The combustion of {eq}1.0 {/eq} pound of oil provides {eq}2.4 \times 10^7 \ J {/eq}.

(a) How many {eq}kg {/eq} of oil are needed to heat {eq}100 \ kg {/eq} of water from {eq}22 {/eq} to {eq}100^\circ \ C {/eq}?

(b) How many {eq}kg {/eq} of oil are needed to provide steam from {eq}100 \ kg {/eq} of water at {eq}100^\circ \ C {/eq}?

## Heating System

One of the most prevalent application of the fundamentals of heat transfer is in the heating system. A heating medium absorbs heat from the combustion source and distributes it using pipeline networks in targeted areas.

{eq}\begin{align*} &\text{a. Amount of oil required relative to specific heat}\\ &m_{oil}=Q_{specific\:heat}\times \frac{lb_{oil}}{Energy_{rate}}\\ &m_{oil}=mCp(T_2-T_1)\times \frac{lb_{oil}}{Energy_{rate}}\\ &m_{oil}=\left(100kg\times 4.184kJ/kg^{o}C\times (100-22)^{o}C\times 1000J/kJ\right) \frac{1.0lbm}{2.4\times 10^{7}J}\\ &m_{oil}=1.3598lbm\\ \\ &\text{b. Amount of oil required relative to latent heat}\\ &m_{oil}=Q_{latent\:heat}\times \frac{lb_{oil}}{Energy_{rate}}\\ &m_{oil}=mLHV\times \frac{lb_{oil}}{Energy_{rate}}\\ &m_{oil}=\left(100kg\times 2260kJ/kg\times 1000J/kJ\right) \frac{1.0lbm}{2.4\times 10^{7}J}\\ &m_{oil}=9.4167lbm\\ \end{align*} {/eq} 