Randall D. Knight — The Micro/Macro Connection: Problem Problem_51

a. Find an expression for the \(v_{\text{rms}}\) of gas molecules in terms of \(p\), \(V\), and the total mass of the gas \(M\). b. A gas cylinder has a piston at one end that is moving outward at speed \(v_{\text{piston}}\) during an isobaric expansion of the gas. Find an expression for the rate at which \(v_{\text{rms}}\) is changing in terms of \(v_{\text{piston}}\), the instantaneous value of \(v_{\text{rms}}\), and the instantaneous value \(L\) of the length of the cylinder. c. A cylindrical sample chamber has a piston moving outward at \(0.50 \text{ m/s}\) during an isobaric expansion. The rms speed of the gas molecules is \(450 \text{ m/s}\) at the instant the chamber length is \(1.5 \text{ m}\). At what rate is \(v_{\text{rms}}\) changing?