Question

One method of estimating the temperature of the center of the sun is based on the assumption that the center consists of gases that have an average molar mass of 2. 00 g/mol. If the density of the center of the sun is 1. 40 g/cm3 at a pressure of 1. 30 x 109 atm, calculate the temperature.

Answer 1

By using ideal gas approximation, the sun's temperature is 2.27 x 10⁷ K.

We need to know about ideal gas to solve this problem. The ideal gas will follow the rule

P . V = n . R . T

where P is pressure, V is volume, n is the amount of substance, R is the ideal gas constant (8.31 J/mol.K) and T is temperature.

From the question above, we know that:

Mr = 2 g/mol

ρ = 1.4 g/cm³

P = 1.3 x 10⁹ atm = 1.32 x 10¹⁴ Pa

m(sun) = 1989 x 10³⁰ g

Find the amount of sun substance

n = m / Mr

n = 1989 x 10³⁰ / 2

n = 994.5 x 10³⁰ mol

Find the volume of sun

V = m/ρ

V = 1989 x 10³⁰ / 1.4

V = 1420.71 x 10³⁰ cm³

V = 1.42 x 10²⁷ m³

By substituting the parameters, we get

P . V = n . R . T

1.32 x 10¹⁴ . 1.42 x 10²⁷ = 994.5 x 10³⁰ . 8.31 . T

T = 2.27 x 10⁷ K

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