From a hot reservoir at a temperature of T 1 , Carnot engine A takes an input he

Question

From a hot reservoir at a temperature ofT1, Carnot engine A takes an input heat of 8110J, delivers 2650 J of work, and rejects heat to a cold reservoirthat has a temperature of 699 K. This cold reservoir at 699 K alsoserves as the hot reservoir for Carnot engine B, which uses therejected heat of the first engine as input heat. Engine B delivers1670 J of work, while rejecting heat to an even colder reservoirthat has a temperature of T2. Find thetemperatures (a)T1 and(b)T2. I have T1=1039K but I cannot get T2 Igot 411.3 K but it is not correct any help is appreciated From a hot reservoir at a temperature ofT1, Carnot engine A takes an input heat of 8110J, delivers 2650 J of work, and rejects heat to a cold reservoirthat has a temperature of 699 K. This cold reservoir at 699 K alsoserves as the hot reservoir for Carnot engine B, which uses therejected heat of the first engine as input heat. Engine B delivers1670 J of work, while rejecting heat to an even colder reservoirthat has a temperature of T2. Find thetemperatures (a)T1 and(b)T2. I have T1=1039K but I cannot get T2 Igot 411.3 K but it is not correct any help is appreciated

Explanation / Answer

   Efficiency ofengine          =   output/input   =   1   -   Tcold/ Thot    a.   For firstengine,   1   =   2650J / 8110J   =   1   -   699/ T1          0.327   =   1   -   699/ T1       699 /T1   =   0.673   =>   T1   =   699/0.673   =   1038.63   ˜   1039   K    b.   For secondengine,   inputheat    =   rejected heat fromfirst engine   =   8110 -2650   =   5460   J       2   =   1670/5460   =   1   -   T2/ 699       0.306   =   1   -   T2/ 699   =>   T2   =   699*0.694   =   485.10   ˜   485   K       699 /T1   =   0.673   =>   T1   =   699/0.673   =   1038.63   ˜   1039   K    b.   For secondengine,   inputheat    =   rejected heat fromfirst engine   =   8110 -2650   =   5460   J       2   =   1670/5460   =   1   -   T2/ 699       0.306   =   1   -   T2/ 699   =>   T2   =   699*0.694   =   485.10   ˜   485   K

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