Project ForgeA Carnot engine (CE-1) works between two temperature reservoirs A and B, where TA=900 K and TB=500 K. A second Carnot engine (CE-2) works between temperature reservoirs B and C, where TC=300 K. In each cycle of CE-1 and CE-2, all the heat rejected by CE-1 to reservoir B is used by CE-2. For one cycle of operation, if the net Q absorbed by CE-1 from reservoir A is 150 MJ, the net heat rejected to reservoir C by CE-2 (in MJ) is __________.
Explanation
CE-1 efficiency = 1−TB/TA = 1−500/900 = 4/9. Work by CE-1 = (4/9)×150 = 66.67 MJ, so heat rejected to B = 150−66.67 = 83.33 MJ — this becomes CE-2's heat input. CE-2 efficiency = 1−TC/TB = 1−300/500 = 0.4. Heat rejected by CE-2 to C = (1−0.4)×83.33 = 50 MJ.
Source: GATE ME 2015 (Session 1) (2015)
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