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A gas is contained in a cylinder with a movable piston. The pressure \(P\), volume \(V\), and temperature \(T\) of the gas satisfy the ideal gas law:$$PV = nRT,$$where \(n\) and \(R\) are constants. The gas is heated so that the temperature increases at a constant rate of \(2\) K/s. At a certain instant, \(T=300\) K, \(V=0.01\) m\(^3\), and \(P=2.5 \times 10^5\) Pa. Assume the piston can move so that the pressure \(P\) remains constant.
Using the ideal gas law, express the volume \(V\) as a function of the temperature \(T\) (since \(P\) is constant).
Find the rate of change of the volume \(\tfrac{dV}{dt}\) when \(T=300\) K.
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