A steel bar in the form of a rectangular parallelepiped of height a, breadth b, and length c is embedded in a cake of ice as shown in Fig. P11-2. With the aid of an external magnetic field, a constant force F is exerted downward on the bar. The whole system is at O°c.
(a) Show that the decrease in temperature of the ice directly below the bar is
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Write My Essay For Me!(b) Ice melts (see Probe 11.12) under the bar, and all the water thus formed is forced to the top of the bar, where it refreezes. This phenomenon is known as regelation. Heat, therefore, is liberated above the bar, is conducted through the metal and a layer of water under the metal, and is absorbed by the ice under the layer of water. Show that the speed with which the bar sinks through the ice is
Where U’ is the overall heat-transfer coefficient of the composite heat-conducting path consisting of the metal and the water layer. U’ is given by
Where Xm and Xw are the thicknesses of the metal and water layer, respectively, and Km and Ki are their respective thermal conductivities.
(c) Assuming that the water layer has a thickness of about 10-5 m and a thermal conductivity of about 0.6 W/m· K, and that the bar is 0.1 m long, with a and b each equal to 10-3 m, with what speed will the bar descend when F = 102 N? (Thermal conductivity of steel is 60W/m· K.)
Problem 11.12
Figure P11-1 shows the surface for the equation of state of water as viewed from the high-temperature end. Consider Ikg of ice in the state i (Pi = 1.01 x 105 Pa, Ti = 273K).
The ice experiences an isentropic compression to a state f:
(a) Why is the state f in the mixture region? In other words, why does some of the ice melt?
(b) Show that the fraction x of ice that is melted is given by
(c) State explicitly the simplifying assumptions that must be made in order that x may be written
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