Thermodynamics

Chapter 7 | 385EXAMPLE 7–19Entropy Generated when a Hot Block Is Droppedin a LakeA 50-kg block of iron casting at 500 K is thrown into a large lake that is at atemperature of 285 K. The iron block eventually reaches thermal equilibriumwith the lake water. Assuming an average specific heat of 0.45 kJ/kg · K forthe iron, determine (a) the entropy change of the iron block, (b) the entropychange of the lake water, and (c) the entropy generated during this process.Solution A hot iron block is thrown into a lake, and cools to the laketemperature. The entropy changes of the iron and of the lake as well as theentropy generated during this process are to be determined.Assumptions 1 Both the water and the iron block are incompressiblesubstances. 2 Constant specific heats can be used for the water and the iron.3 The kinetic and potential energy changes of the iron are negligible, KE PE 0 and thus E U.Properties The specific heat of the iron is 0.45 kJ/kg K (Table A–3).Analysis We take the iron casting as the system (Fig. 7–67). This is a closedsystem since no mass crosses the system boundary during the process.To determine the entropy change for the iron block and for the lake, firstwe need to know the final equilibrium temperature. Given that the thermalenergy capacity of the lake is very large relative to that of the iron block, thelake will absorb all the heat rejected by the iron block without experiencingany change in its temperature. Therefore, the iron block will cool to 285 Kduring this process while the lake temperature remains constant at 285 K.(a) The entropy change of the iron block can be determined fromLAKE285 KIRONCASTINGm = 50 kgT 1 = 500 KFIGURE 7–67Schematic for Example 7–19.T 2¢S iron m 1s 2 s 1 2 mc avg lnT 1 150 kg2 10.45 kJ>kg # K2 ln285 K500 K 12.65 kJ/K(b) The temperature of the lake water remains constant during this process at285 K. Also, the amount of heat transfer from the iron block to the lake isdetermined from an energy balance on the iron block to beE in E out ¢E systemorNet energy transferby heat, work, and massThen the entropy change of the lake becomes¢S lake Q lakeT lake⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭Change in internal, kinetic,potential, etc., energiesQ out ¢U mc avg 1T 2 T 1 2Q out mc avg 1T 1 T 2 2 150 kg210.45 kJ>kg # K21500 2852 K 4838 kJ4838 kJ285 K 16.97 kJ /K