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It is desired to produce the vapor of a volatile liquid at a steady rate by boiling it in a small spherical vessel, as pictured to the right. The boiling vessel consists of a spherical shell of inside radius Ri = 5 cm and outside radius Ro= 10 cm, with a small side-port for feeding in the liquid, and a small vent at the top for the vapor to leave. The vessel wall produces a uniform volumetric generation of heat, S (by means of electrical heating), and its outside surface at Ro is completely insulated so that all the heat generated goes toward vaporizing the liquid.a. It is desired to produce vapor at the rate of 1.50 mol/min, and the latent heat of its vaporization is 3,500 cal/mole. The boiling point is 180°C. Evaluate the required strength of the volumetric heat source S (cal/cm3·s). (Neglect any sensible heat effects.)b. The thermal conductivity of the material of the vessel is k = 0.012 cal/s·cm·K. Derive and plot the radial temperature profile T(r) in the layer, and in particular, determine the temperature at the outside surface, Ro.

It is desired to produce the vapor of a volatile liquid at a steady rate by boiling it in a small spherical vessel, as pictured to the right. The boiling vessel consists of a spherical shell of inside radius Ri = 5 cm and outside radius Ro= 10 cm, with a small side-port for feeding in the liquid, and a small vent at the top for the vapor to leave. The vessel wall produces a uniform volumetric generation of heat, S (by means of electrical heating), and its outside surface at Ro is completely insulated so that all the heat generated goes toward vaporizing the liquid.a. It is desired to produce vapor at the rate of 1.50 mol/min, and the latent heat of its vaporization is 3,500 cal/mole. The boiling point is 180°C. Evaluate the required strength of the volumetric heat source S (cal/cm3·s). (Neglect any sensible heat effects.)b. The thermal conductivity of the material of the vessel is k = 0.012 cal/s·cm·K. Derive and plot the radial temperature profile T(r) in the layer, and in particular, determine the temperature at the outside surface, Ro.

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