91Ó°ÊÓ

A tank containing 20 kg of water at \(293.15 \mathrm{K}\left(20^{\circ} \mathrm{C}\right)\) is fitted with a stirrer that delivers work to the water at the rate of \(0.25 \mathrm{kW}\). How long does it take for the temperature of the water to rise to \(303.15 \mathrm{K}\left(30^{\circ} \mathrm{C}\right)\) if no heat is lost from the water? For water, \(C_{P}=\) \(4.18 \mathrm{kJ} \mathrm{kg}-^{\circ} \mathrm{C}^{-1}\).

Nitrogen flows at steady state through a horizontal, insulated pipe with inside diameter of \(38.1 \mathrm{mm} .\) A pressure drop results from flow through a partially opened valve. Just upstream from the valve the pressure is \(690 \mathrm{kPa}\), the temperature is \(322.15 \mathrm{K}\left(49^{\circ} \mathrm{C}\right)\) and the average velocity is \(6.09 \mathrm{m}\) s '. If the pressure just downstream from the valve is \(138 \mathrm{kPa}\), what is the temperature? Assume for nitrogen that \(\mathrm{PV} / \mathrm{T}\) is constant, \(C_{V}=\) \((5 / 2) R,\) and \(C_{P}=(7 / 2) R .\) (Values for \(R\) are given in App. A.)

Water flows through a horizontal coil heated from the outside by high- temperature flue gases. As it passes through the coil the water changes state from liquid at \(200 \mathrm{kPa}\) and \(353.15 \mathrm{K}\left(80^{\circ} \mathrm{C}\right)\) to vapor at \(100 \mathrm{kPa}\) and \(398.15 \mathrm{K}\left(125^{\circ} \mathrm{C}\right)\). Its entering velocity is \(3 \mathrm{m} \mathrm{s}^{-1}\) and its exit velocity is \(200 \mathrm{m} \mathrm{s}^{-1}\). Determine the heat transferred through the coil per unit mass of water. Enthalpies of the inlet and outlet streams are: Inlet: \(334.9 \mathrm{kJ}\) kg-'; Outlet: \(2726.5 \mathrm{kJ} \mathrm{kg}^{-1}\).

Find the equation for the work of a reversible, isothermal compression of 1 mol of gas in a piston/cylinder assembly if the molar volume of the gas is given by $$V=\frac{R T}{P}+b$$ where \(b\) and \(R\) are positive constants.