Dry air at a constant temperature of \(20^{\circ} \mathrm{C}(293 \mathrm{~K})\) passes through a valve into a rigid cubic container of \(1 \mathrm{~m}\) on each side (Figure 7.2). The pressure \(p_{\mathrm{i}}\) at the inlet of the valve is constant, and it is greater than \(p\). The valve resistance is approximately linear, and \(R=1000 \mathrm{~Pa} \cdot \mathrm{s} / \mathrm{kg}\). Assume that the filling process is isothermal. Develop a mathematical model of the pressure \(p\) in the container.

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Pi P.P FIGURE 7.2 A pneumatic system with a rigid cubic container. V