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Distribution of granular temperatures in granular gas mixtures isinvestigated analytically and numerically. We analyze space uniform systems ina homogeneous cooling state (HCS) and under a uniform heating with amass-dependent heating rate $\Gamma_k\sim m_k^{\gamma}$. We demonstrate thatfor steep size distributions of particles the granular temperatures obey auniversal power-law distribution, $T_k \sim m_k^{\alpha}$, where the exponent$\alpha$ does not depend on a particular form of the size distribution, thenumber of species and inelasticity of the grains. Moreover, $\alpha$ is auniversal constant for a HCS and depends piecewise linearly on $\gamma$ forheated gases. The predictions of our scaling theory agree well with thenumerical results.

Universality of temperature distribution in granular gas mixtures with a steep particle size distribution