The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding 10⁷ 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 = ³⁰ kg, radius of the Sun = ⁸ m.
The mass density of the Sun is approximately ³ kg/m³, which lies in the range of densities of solids and liquids, not gases. This is contrary to the initial expectation that a hot plasma would have gas-like density.
Calculation: Given: Mass of Sun = ³⁰ kg, Radius of Sun = ⁸ m
Volume of Sun (assuming spherical shape): V = (4/3)πr³ = (4/3) × π × (⁸)³ V = (4/3) × π × ²⁴ = ²⁷ m³
Density of Sun: ρ = Mass/Volume = ³⁰ / ²⁷ ρ ³ kg/m³
This density is comparable to solids and liquids (water has density ~10³ kg/m³), whereas gases have densities around 1 kg/m³. Despite being a hot plasma at extremely high temperatures, the Sun's immense gravitational compression results in a density similar to solids and liquids.
Explanation
This question tests understanding of density calculation and comparison with different states of matter. Students often incorrectly assume that since the Sun is plasma (ionized gas), its density should be gas-like. However, the calculation shows that gravitational compression makes the Sun's density comparable to solids and liquids. The key learning is that temperature alone doesn't determine density—gravitational forces play a crucial role in stellar objects.
Solution Steps
Step 1: Identify given data - Mass = ³⁰ kg, Radius = ⁸ m
Step 2: Calculate volume using sphere formula V = (4/3)πr³
Step 3: Substitute r = ⁸ m to get V = ²⁷ m³
Step 4: Calculate density ρ = Mass/Volume = ³⁰ / ²⁷
Step 5: Compare result ($\approx$$$1.4 \times 10$$³ kg/m³) with typical densities of solids (~10³-10⁴ kg/m³), liquids (~10³ kg/m³), and gases (~1 kg/m³)