High-Temperature Expansion for the Orientational Specific Heat of Solid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Terms up to order ${(\frac{\ensuremath{\Gamma}}{{k}_{B}T})}^{5}$ in the high-temperature expansion of the orientational specific heat of ortho-para alloys of solid ${\mathrm{H}}_{2}$ or ${\mathrm{D}}_{2}$ are evaluated. Good agreement is obtained between theory and experiment using a Pad\'e approximant and effective values of the quadrupolar coupling constant, $\frac{{\ensuremath{\Gamma}}_{\mathrm{eff}}}{{\ensuremath{\Gamma}}_{0}}=0.83$ for ${\mathrm{D}}_{2}$ and $\frac{{\ensuremath{\Gamma}}_{\mathrm{eff}}}{{\ensuremath{\Gamma}}_{0}}=0.80$ for ${\mathrm{H}}_{2}$, where ${\ensuremath{\Gamma}}_{0}$ is the value for a rigid lattice. These values agree with other determinations of ${\ensuremath{\Gamma}}_{\mathrm{eff}}$, whereas the ${T}^{\ensuremath{-}2}$ approximation for the specific heat yields anomalously small values of ${\ensuremath{\Gamma}}_{\mathrm{eff}}$.

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