Question

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding $10^7$ K, and its outer surface at a temperature of about 6000 K. At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases ? Check if your guess is correct from the following data : mass of the Sun = $2.0$ ×$10^{30}$ kg, radius of the Sun = $7.0$× $10^8$m.

Answer 1

Mass of the Sun, $\text M$ = $2.0\times 10^{30}\;\text {kg}$
Radius of the Sun,$\text R$ = $7.0\times 10^{8}\;\text {m}$
Volume of the Sun, $\text V$ = $\frac{4}{3}\pi \text R^3$

= $\frac{4}{3}\times \frac{22}{7}\times (7.0\times 10^8)^3$

= $\frac{88}{21}\times 343\times 10^{24}$ = $1437.3\times 10^{24}\; \text m^3$
Density of the Sun = $\frac{\text{Mass}}{\text{ Volume}}$ = \frac{2.0\times 10^{30}}{1437.3\times 10^{24}}$$\sim $1.4\times 10^3\; \text {kg}/\text m^5$

The density of the Sun is in the density range of solids and liquids. This high density is attributed to the intense gravitational attraction of the inner layers on the outer layer of the Sun.