(1 point) As a result of radioactive decay, heat is generated uniformly throughout the interior of the earth at a rate of around 30 watts per cubic kilometer. (A watt is a rate of heat production.) T...
(1 point) As a result of radioactive decay, heat is generated uniformly throughout the interior of the earth at a rate of around 30 watts per cubic kilometer. (A watt is a rate of heat production.) The heat then flows to the earth's surface where it is lost to space. Let F(z,y, z denote the rate of flow of heat measured in watts per square kilometer. By definition, the flux of F across a surface is the quantity of heat flowing through the surface per unit of time (a) Suppose that the actual heat generation is 27W/km3 What is the value of div F? div F- Include units) (b Assume the heat flows outward symmetrically. Verify that F zi + 3 herer +2 and α is a suitable constant, sats es e given conditions. Find a α7, (Include units.) (c) Let T z y, z denote the temperature inside the earth. Heat flows according to the equation F -k grad T where k is a constant IT is in °C then k Assuming the earth is a sphere with radius 6400 km and surface temperature 20°C, what is the temperature at the center? 27,0 C/km. (degrees C)
(1 point) As a result of radioactive decay, heat is generated uniformly throughout the interior of the earth at a rate of around 30 watts per cubic kilometer. (A watt is a rate of heat production.) The heat then flows to the earth's surface where it is lost to space. Let F(z,y, z denote the rate of flow of heat measured in watts per square kilometer. By definition, the flux of F across a surface is the quantity of heat flowing through the surface per unit of time (a) Suppose that the actual heat generation is 27W/km3 What is the value of div F? div F- Include units) (b Assume the heat flows outward symmetrically. Verify that F zi + 3 herer +2 and α is a suitable constant, sats es e given conditions. Find a α7, (Include units.) (c) Let T z y, z denote the temperature inside the earth. Heat flows according to the equation F -k grad T where k is a constant IT is in °C then k Assuming the earth is a sphere with radius 6400 km and surface temperature 20°C, what is the temperature at the center? 27,0 C/km. (degrees C)