Question

The sun radiates $\mathbf{3}\mathbf{.}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}\mathbf{J}$of energy into space every second. What is the rate at which mass is lost from the sun?

Short answer

The rate at which mass is lost from the sun is $4.3\times {10}^6{\mathrm{kgs}}^{-1}$.

Step-by-step solution

Einstein’s mass energy relation.

The Einstein mass energy is used to evaluate the relation between mass and energy in a system. This equation can be represented as:

${\mathbf{\text{ΔE=Δm·c}}}^{\mathbf{2}}$

Where,

• $\mathbf{\text{ΔE}}$=change in energy
• $\mathbf{\text{Δm}}$=change in mass
• ${\mathbf{\text{c}}}^{\mathbf{2}}$=velocity of light

Determine the rate at which mass is lost from the sun.

The Einstein mass energy equation is represented by the following equation:

$\Delta E=\Delta m.c^2\dots \dots ..\left(1\right)$

Put the values in (1) to calculate the mass.

$\begin{array}{c}\Delta m=\frac{\Delta E}{c^2}\\ =\frac{3.9\times {10}^{23}\mathrm{J}}{{\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right)}^2}\\ =4.3\times {10}^6\mathrm{kg}\end{array}$

Thus, the rate at which mass is lost from the sun is $4.3\times {10}^6\mathrm{kg}.{\mathrm{s}}^{-1}$.