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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.


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Last updated date: 21st Jun 2024
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Answer
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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.


Additional Note:

The Sun is so massive that its gravity is strong enough to hold its plasma together. However, if the Sun were not so massive, its plasma would escape into space.


Note:

The mass density of the Sun is not uniform throughout its interior. It is highest in the core and decreases towards the surface. However, even the mass density of the Sun's core is within the range of densities of gases.