= Solution
For a fully ionized, nonrelativistic monatomic <ideal gas>, $\gamma=5/3$ and the <virial theorem> becomes
$$
\boxed{\Omega=-2U,\qquad E=U+\Omega=-U.}
$$
Since $U$ increases with its particle-weighted mean <temperature>, the equilibrated self-gravitating object has <negative heat capacity>: adding total <energy> allows expansion, makes $\Omega$ less negative, and reduces $U$. Conversely, radiating energy permits contraction and raises the internal temperature. This refers to a sequence of gravitational equilibria, not to the positive local heat capacity of a parcel at fixed volume.
In an ordinary nondegenerate nuclear-burning star, a rise in nuclear heating tends to expand and cool the burning region, lowering its temperature-sensitive reaction rate. Reduced heating leads to contraction and reheating. This expansion feedback is the nuclear thermostat; it can fail in degenerate matter where pressure responds weakly to temperature. During contraction of a <pre-main-sequence star>, gravitational binding supplies the radiated <luminosity> and heats the interior. For a fixed-structure scaling, half the released gravitational energy increases $U$ and half escapes as radiation, until hydrogen burning can support a long-lived <main sequence> equilibrium.
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