Question

In: Physics

An ideal heat engine takes in heat from a reservoir at 330 °C and has an...

An ideal heat engine takes in heat from a reservoir at 330 °C and has an efficiency of 31%. If the exhaust temperature does not vary and the efficiency is increased to 42%, what would be the increase in the temperature of the hot reservoir?


please answer !!

Solutions

Expert Solution

Solution :-

Case I:

T1 = 330 °c

     = 603 K

Efficiency = (T1 - T2) / T1

0.31 = ( 603 - T2) / 603

186.93 = 603 - T2

T2 = 416 K

Case II:

Temeprature of reservoir = T1'

Efficiency = (T1' - T2 ) / T1'

0.42 = ( T1' - 416 ) / T1'

0.42T1' = T1' - 416

T1' ( 1 - 0.42) = 416

T1' = 416 / 0.58

      = 717.24 K

      = (717.24- 273) deg c

      = 444.24 degc

Increase in the temperature of hot reservoir = T1' - T1

                                                                  = 444.24 - 330

                                                                  = 111.24 deg


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