A quasi-gasdynamic system of equations with a mass force and a heat source is well known in the case of the perfect polytropic gas. In the paper, the system is extended to the case of general equations of gas state satisfying thermodynamic stability conditions. The entropy balance equation is studied. The validity of the non-negativity property is algebraically analyzed for the entropy production. Two different forms are derived for its relaxation summands. It is proved that under a condition on the heat source intensity, the non-negativity property is valid.

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