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Thermodynamics
First Law of Thermodynamics
GATE 2009
Hard

An irreversible heat engine extracts heat from a high temperature source at a rate of 100 kW and rejects heat to a sink at a rate of 50 kW. The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at 17°C and 75°C. The rate (in kW) at which the heat pump delivers heat to its high temperature sink is

  • A50
  • B250
  • 300
  • D360

Explanation

Engine work output W=100-50=50 kW. The reversible heat pump's COP (heating)=Thigh/(Thigh-Tlow)=348/(348-290)=348/58=6.0. Heat delivered to the high-temperature sink=COP×W=6.0×50=300 kW.

Source: GATE ME 2009 (2009)

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