FrontierScience / bb0539ef-d9fd-4215-bf16-b0eca44a8778 / | Parameter | Value |

| Parameter | Value |
| --- | --- |
| `m_(p)` (proton mass) | `1.67×10^(−27)kg` |
| `M` (solar mass) | `1.989×10³⁰kg` |
| `R` (solar radius) | `6.955×10⁸m` |
| `G` (gravitational constant) | `6.674×10^(−11)N•m²/kg²` |
| `k` (Boltzmann’s constant) | `1.381×10^(−23)J/K` |

| `m_(e)`(mass of electron) | `\( 9.12 × 10^{-31} kg \)` |

Make use of any relevant values if required for calculation.

We are given that the average pressure of the Sun `⟨P⟩=−(U_(g))/(3V)`, where `V` is the total volume and `U_(g)` is the total gravitational potential energy of the sun. Assume that the mass of the sun is distributed uniformly.

Assuming that the Sun can be regarded as composed of an ideal gas, find the average temperature `⟨T⟩` of the Sun in Kelvins supposing that the Sun consists of only equal numbers of protons and electrons. Leave your answer to 3 significant figures.

Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.

| Parameter | Value |
| --- | --- |
| `\( m_p \)` (proton mass) | `\( 1.67 \times 10^{-27} kg \)` |
| `\( M \)` (solar mass) | `\( 1.989 \times 10^{30} kg \)` |
| `\( R \)` (solar radius) | `\( 6.955 \times 10^8 m \)` |
| `\( G \)` (gravitational constant) | `\( 6.674 \times 10^{-11} N \bullet m^2/kg^2 \)` |
| `\( k \)` (Boltzmann’s constant) | `\( 1.381 \times 10^{-23} J/K \)` |

| `\( m_e \)`(mass of electron) | `\( 9.12 × 10^{-31} kg \)` |

Make use of any relevant values if required for calculation.

We are given that the average pressure of the Sun `\( \langle P \rangle = -\frac{U_g}{3V} \)`, where `\( V \)` is the total volume and `\( U_g \)` is the total gravitational potential energy of the sun. Assume that the mass of the sun is distributed uniformly.

Assuming that the Sun can be regarded as composed of an ideal gas, find the average temperature `\( \langle T \rangle \)` of the Sun in Kelvins supposing that the Sun consists of only equal numbers of protons and electrons. Leave your answer to 3 significant figures.

Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.