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To derive the expression for the mean temperature \(\langle T \rangle\) in a star, we can use basic principles from stellar structure, including the Virial theorem and hydrostatic equilibrium. ### Step 1: Using the Virial Theorem The Virial theorem states that for a self-gravitating system in equilibrium: \[ 2K + U = 0 \] where: - \( K \) is the total kinetic energy (thermal energy in the case of a star), - \( U \) is the gravitational potential energy. Since thermal energy in a star is mainly due to the pressure from an ideal ________ ________ ____ ________ __________ ______ ____ _______ _________.
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