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

Idea / Expectation:

The Sun is at an extremely high temperature (core ≳ 10⁷ K, surface ≈ 6000 K), so matter exists as a plasma, not as a solid or liquid.

At such temperatures, one might expect the Sun’s matter to behave like a gas, and hence its average mass density to be comparable to or only slightly higher than that of gases, rather than solids or liquids.

Let us check this expectation quantitatively.

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Given:

Mass of the Sun, M = 2.0 × 10³⁰ kg
Radius of the Sun, R = 7.0 × 10⁸ m

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Step 1: Calculate the volume of the Sun

Assuming the Sun to be spherical:

V = (4/3)πR³

V = (4/3)π (7.0 × 10⁸)³

V ≈ 1.44 × 10²⁷ m³

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Step 2: Calculate the average mass density

Average density, ρ = M / V

ρ = (2.0 × 10³⁰) / (1.44 × 10²⁷)

ρ ≈ 1.39 × 10³ kg m⁻³

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Step 3: Compare with known densities

• Density of air ≈ 1.2 kg m⁻³
• Density of water ≈ 1.0 × 10³ kg m⁻³
• Density of typical solids ≈ 10³ – 10⁴ kg m⁻³

The Sun’s average density is of the same order as that of liquids (like water) and much higher than gases.

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Conclusion:

Although the Sun is entirely in the plasma (gaseous) state due to its very high temperature, its enormous gravitational compression makes its average mass density comparable to that of liquids, not gases.

Thus, our initial expectation based only on temperature is not correct; gravity plays a dominant role in determining the Sun’s density.