Chapter 31, Problem 60GP

To determine

Heat of combustion per kilogram of hydrogen fuel.

Answer to Problem 60GP

The heat of combustion of hydrogen fuel is $6.3\times {10}^{14}\text{J/kg}$ and in comparison to coal it is $2.1\times {10}^7$ times higher.

Explanation of Solution

Given info:

Escape energy of neutrinos is $0.5\text{ MeV}$

Remaining energy of the Sun is $26.2\text{ MeV}$

Heat of combustion of coal is $3\times {10}^7\text{J/kg}$

Eq-31-7: $4\text{H}\to \text{H}\text{e}+2{\mathrm{e}}^{+}+2\mathrm{\nu }+2\mathrm{\gamma }$

Calculation:

Mass of proton is $1.008\text{ u}$

Conversion of MeV into joules, we get:

Remaining energy is given by:

  $\begin{array}{l}=26.2\times {10}^6\times 1.6\times {10}^{-19}\text{J}\\ =41.92\times {10}^{-13}\text{J}\end{array}$

So, the heat of combustion can be calculated as follows:

  $\begin{array}{l}=\frac{\left(41.92\times {10}^{-13}\text{J}\right)}{4\left(1.008\text{ u}\right)\left(1.67\times {10}^{-27}\text{kg}\right)}\\ =6.3\times {10}^{14}\text{J/kg}\end{array}$

Comparison of heat of combustion of both cases is given by:

  $\begin{array}{l}=\frac{6.3\times {10}^{14}\text{J/kg}}{3\times {10}^7\text{J/kg}}\\ =2.1\times {10}^7\end{array}$

Conclusion:

Thus, the heat of combustion of hydrogen fuel is $6.3\times {10}^{14}\text{J/kg}$ and in comparison to coal it is $2.1\times {10}^7$ times higher.