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A closed cubical box made of a perfectly insulating material has walls of thickness 8 cm and the only way for the heat to enter or leave the box is through two solid cylinderical metal plugs , each of cross - sectional area 12 cm^(2) and length 8 cm fixed in the opposite walls of the box . The outer surface A of one plug is kept at a temperature of 100^(@)C while the outer surface of the other plug is maintained at a temperature of 4^(@)C~. The thermal coinductivity of the material of the plug is 0.5 cal // cmsec""^(@)C. A source of energy generating 36 cal s^(-1) is enclosed inside the box . Find the equilibrium temperature of the inner surface of the box assuming that it is the same at all points on the inner surface |
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Answer» Solution :At equilibrium, the total energy generated by the source per second is equal to the HEAT leaving per second through the two metal plugs (Figure-4.12). Let T°C be the equilibrium temperature. Then heat leaving the box per second through surface A `(k(T-100)xx12)/(8)cals^(-1)` Heat leaving the box per second through the surface B `(k(T-4)xx12)/(8)cals^(-1)` Hence `(12k)/(8)(T-100+T-4)=36` or `2T-104=(36xx8)/(12k)=(36xx8)/(12xx0.5)=48 or T=76^(@)C` |
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