Consider a star of mass M = 10M⊙, composed entirely of fully ionized 12C. Its core temperature is Tc = 6 × 108 K (compared to Tc,⊙ = 1.5 × 107 K for the Sun). Use the classical ideal gas law, the dimensional relation between mass, density, and radius, and the virial theorem to find the scaling of the stellar radius r∗ with total mass M, mean particle mass m , and core temperature Tc. Using the values of these parameters for the Sun, find the radius of the star.

Consider a star of mass M = 10M⊙, composed entirely of fully ionized 12C. Its core temperature is Tc = 6 × 108 K (compared to Tc,⊙ = 1.5 × 107 K for the Sun). Use the classical ideal gas law, the dimensional relation between mass, density, and radius, and the virial theorem to find the scaling of the stellar radius r∗ with total mass M, mean particle mass m , and core temperature Tc. Using the values of these parameters for the Sun, find the radius of the star.

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Question

Consider a star of mass M = 10M_⊙, composed entirely of fully ionized ¹²C. Its core temperature is T_c = 6 × 10⁸ K (compared to T_c,⊙ = 1.5 × 10⁷ K for the Sun).

Use the classical ideal gas law, the dimensional relation between mass, density, and radius, and the virial theorem to find the scaling of the stellar radius r_∗ with total mass M, mean particle mass m , and core temperature T^c. Using the values of these parameters for the Sun, find the radius of the star.

Definition Definition Any of various laws that describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. At a constant temperature, the pressure of a particular amount of gas is inversely proportional with its volume (Boyle's Law) In a closed system with constant pressure, the volume of an ideal gas is in direct relation with its temperature (Charles's Law) At a constant volume, the pressure of a gas is in direct relation to its temperature (Gay-Lussac's Law) If the volume of all gases are equal and under the a similar temperature and pressure, then they contain an equal number of molecules (Avogadro's Law) The state of a particular amount of gas can be determined by its pressure, volume and temperature (Ideal Gas law)

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