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The combustion heat is,$E=3.3x{10}^{7}J/\mathrm{kg}$ .

The mass of the Sun is,$m=2.0x{10}^{30}\mathrm{kg}$ .

The power is, $P=3.9x{10}^{26}W$.

The expression for the number of atom in mass of mis given by,

$\mathbf{N}\mathbf{=}\frac{{\mathbf{mN}}_{\mathbf{A}}}{\mathbf{M}}$

Here, $\mathit{m}$is mass of Sun, ${\mathit{N}}_{\mathbf{A}}$is Avogadro number, and $\mathit{M}$is molar mass of carbon.

The expression for the heat of combustion per atom in terms of energy is given by,

$\begin{array}{l}{\mathbf{E}}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{E}}{\mathbf{N}}\\ \mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{E}\mathbf{M}}{\mathbf{m}{\mathbf{N}}_{\mathbf{A}}}\end{array}$ ...(i)

Here, $\mathit{E}$is energy.

Substitute all the known values in equation (i).

$$\begin{gathered} E_N=\frac{\left(3.3脳{10}^{7}J\right)\left(12.0g/mol\right)}{\left(1000g\right)\left(6.022脳{10}^{23}mo{l}^{-1}\right)} \\ =6.576脳{10}^{-19}J \\ =\left(6.576脳{10}^{-19}J\right)\left(\frac{1eV}{1.6脳{10}^{-19}J}\right) \\ =4.1eV/atom \end{gathered}$$

Therefore, the heat of combustion per atom in terms of energy is$4.1eV/atom$ .

In each event, two oxygen atoms combine with one carbon atom to form carbon dioxide, so the mass of the reactants is,

$2\left(16.0g\right)+12u=44u$

The number of atoms in of reactants is,

$$\begin{gathered} N_r=\frac{\left(1000g\right)\left(6.022脳{10}^{23}mo{l}^{-1}\right)}{44g/mol} \\ =1.37脳{10}^{25} \end{gathered}$$

The energy per kilogram of the initial reactants is given by,

$E_r=N_r{E}_N$ ...(ii)

Substitute all the known values in equation (ii).

$$\begin{gathered} E_r=\left(1.37脳{10}^{25}\right)\left(6.576脳{10}^{-19}J\right) \\ =9.00脳{10}^{6}J \\ =9.00MJ/kg \end{gathered}$$

Therefore, the required energy is $9.00MJ/kg$.

Let $P$be the power output of the Sun.

The burn time of the sun is given by,

$t=\frac{E_s}{P}$ ...(iii).

Here, $E_s$is the energy produced by the mass of the sun.

Find the number of reactants atoms in the mass of sun.

$$\begin{gathered} N_s=\frac{\left(2脳{10}^{33}g\right)\left(6.22脳{10}^{23}mo{l}^{-1}\right)}{44g/mol} \\ =2.74脳{10}^{55} \end{gathered}$$

Find the energy produced by the mass of the sun.

$$\begin{gathered} E_s=N_s{E}_N \\ =\left(2.74脳{10}^{55}\right)\left(6.576脳{10}^{-19}J\right) \\ =1.802脳{10}^{37}J \end{gathered}$$

Substitute all the known values in equation (3).

$$\begin{gathered} t=\frac{1.802脳{10}^{37}J}{3.9脳{10}^{26}W} \\ =4.62脳{10}^{10}s \\ =\left(4.62脳{10}^{10}s\right)\left(\frac{1y}{12脳30脳24脳3600s}\right) \\ 鈮�1.5脳{10}^{3}y \end{gathered}$$

Therefore, the required time is $1.5脳{10}^{3}y$.