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## Question

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 = 2.0 ×1030 kg, radius of the Sun = 7.0 × 108m.

Last updated date: 21st Jun 2024
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### Hint:

The Sun is a hot plasma, which means that its matter is in a gaseous state. Therefore, we expect the mass density of the Sun to be similar to the mass density of gases.

### Step-by-step solution:

Calculate the mass density of the Sun using the following formula:

Mass density = mass/volume

Mass density of the Sun $= \dfrac{(2.0 \times 10^{30} kg)}{\dfrac{4}{3}\pi \times (7.0 \times 10^8 m)^3}$

Mass density of the Sun $= 1.40 \times 10^3 kg/m^3$

Compare the mass density of the Sun to the range of densities of solids and liquids and gases.

The range of densities of solids and liquids is typically between $10^3 kg/m^3$ and $10^4 kg/m^3$. The range of densities of gases is typically between $10^{-3} kg/m^3$ and $10 kg/m^3$.

### Conclusion:

The mass density of the Sun $1.4 \timea 10^3 kg/m^3$ is within the range of densities of gases.