Chapter 7, Problem 7.12P

To determine

(a)

The high heat value in terms of moisture free.

Answer to Problem 7.12P

The high heat value in terms of moisture free is $7506.6\text{Btu}/\text{lb}$ .

Explanation of Solution

Given:

Moisture content is $20\%$ .

Weight of sample placed in calorimeter is $1.2\text{g}$ .

Gross calorific value is $6200\text{Btu}/\text{lb}$ .

Weight of ash that remains in the bomb calorimeter after combustion is $0.3\text{g}$ .

Concept Used:

The moisture heat is subtracted from the original heat energy in case of moisture free condition.

Calculation:

Write the expression for high heat value in moisture free condition.

  $HH{V}_1=\frac{\left(HH{V}_0\times M_0\right)-\left(H{V}_{\text{water}}\times M_{\text{water}}\right)}{M_0-M_{\text{water}}}$   ...... (I)

Here, high heat value in moisture free condition is $HH{V}_1$ , original mass is $M_0$ , original heat value is $HH{V}_0$ , mass of water content is

  $M_{\text{water}}$ and latent heat of evaporation for water is $H{V}_{\text{water}}$ .

Convert the mass of the sample to pounds.

  $\begin{array}{c}1.2\text{g}=\left(1.2\text{g}\right)\left(\frac{0.0022046\text{lb}}{1\text{g}}\right)\\ =2.65\times {10}^{-3}\text{lb}\end{array}$

Substitute, $2.65\times {10}^{-3}\text{lb}$ for $M_0$ , $6200\text{Btu}/\text{lb}$ for $HH{V}_0$ , $20\%$ of $M_0$ for $H{V}_{\text{water}}$ and $974\text{Btu/lb}$ for $H{V}_{\text{water}}$ in Equation (I).

  $\begin{array}{c}HH{V}_1=\frac{\left(6200\text{Btu}/\text{lb}\times 2.65\times {10}^{-3}\text{lb}\right)-\left(974\text{Btu}/\text{lb}\times \left(0.20\times 2.65\times {10}^{-3}\text{lb}\right)\right)}{2.65\times {10}^{-3}\text{lb}-\left(0.20\times 2.65\times {10}^{-3}\text{lb}\right)}\\ =\frac{15.914\text{Btu}}{2.12\times {10}^{-3}\text{lb}}\\ =7506.6\text{Btu}/\text{lb}\end{array}$

Conclusion:

Thus, the high heat value in moisture free condition is $7506.6\text{Btu}/\text{lb}$ .

To determine

(b)

The high heat value in moisture free and ash free conditions.

Answer to Problem 7.12P

The high heat value in moisture free and ash free condition is $9543.8\text{Btu}/\text{lb}$ .

Explanation of Solution

Concept Used:

The moisture heat and the ash heat is subtracted from the original heat energy in case of moisture free and ash free condition.

Calculation:

Write the expression for the high heat value in moisture free and ash free condition.

  $HH{V}_2=\frac{\left(HH{V}_0\times M_0\right)-\left(H{V}_{\text{water}}\times M_{\text{water}}\right)-\left(H{V}_{\text{ash}}\times M_{\text{ash}}\right)}{M_0-M_{\text{water}}-M_{\text{ash}}}$   ...... (II)

Here, high heat value in moisture free and ash free condition is $HH{V}_2$ , original mass is $M_0$ , original heat value is $HH{V}_0$ , mass of water content is $M_{\text{water}}$ , latent heat of evaporation for water is $H{V}_{\text{water}}$ , mass of ash content is $M_{\text{ash}}$ and value of heat for ash is $H{V}_{\text{ash}}$ .

Convert the mass of ash to pounds.

  $\begin{array}{c}0.3\text{g}=\left(0.3\text{g}\right)\left(\frac{0.0022046\text{lb}}{1\text{g}}\right)\\ =6.6\times {10}^{-4}\text{lb}\end{array}$

Substitute, $2.65\times {10}^{-3}\text{lb}$ for $M_0$ , $6200\text{Btu/lb}$ for $HH{V}_0$ , $20\%$ of $M_0$ for $H{V}_{\text{water}}$ , $974\text{Btu/lb}$ for $H{V}_{\text{water}}$ , $6.6\times {10}^{-4}\text{lb}$ for $M_{\text{ash}}$ and $3000\text{Btu/lb}$ for $H{V}_{ash}$ in Equation (II).

  $\begin{array}{c}HH{V}_2=\frac{\left[\begin{array}{l}\left(6200\text{Btu}/\text{lb}\times 2.65\times {10}^{-3}\text{lb}\right)-\left(974\text{Btu}/\text{lb}\times \left(0.20\times 2.65\times {10}^{-3}\text{lb}\right)\right)\\ -\left(3000\text{Btu}/\text{lb}\times 6.6\times {10}^{-4}\text{lb}\right)\end{array}\right]}{2.65\times {10}^{-3}\text{lb}-\left(0.20\times 2.65\times {10}^{-3}\text{lb}\right)-6.6\times {10}^{-4}\text{lb}}\\ =\frac{13.934\text{Btu}}{1.46\times {10}^{-3}\text{lb}}\\ =9543.8\text{Btu}/\text{lb}\end{array}$

Conclusion:

The value of the high temperature of heat in moisture free and ash free condition is calculated using the concept of subtracting moisture free and ash heat from original energy.