A Carnot engine working on a satellite in outer space has to deliver a fixed amount of power at rate W. The temperature of the heat source is also fixed, at T₁. The lower temperature reservoir at T2 consists of a large body of area A; its temperature is maintained at T₂ because it radiates energy into space as much heat as is delivered to it by the engine. The rate of this radiation is σAT2 where σ is a constant. The Carnot engine has to be designed so that, for a given Wand T₁, A has a minimum value. Show that A has a minimum value when T₂ takes the value 3T₁/4.
A Carnot engine working on a satellite in outer space has to deliver a fixed amount of power at rate W. The temperature of the heat source is also fixed, at T₁. The lower temperature reservoir at T2 consists of a large body of area A; its temperature is maintained at T₂ because it radiates energy into space as much heat as is delivered to it by the engine. The rate of this radiation is σAT2 where σ is a constant. The Carnot engine has to be designed so that, for a given Wand T₁, A has a minimum value. Show that A has a minimum value when T₂ takes the value 3T₁/4.
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![A Carnot engine working on a satellite in outer space has to deliver a
fixed amount of power at rate W. The temperature of the heat source is
also fixed, at T₁. The lower temperature reservoir at T2 consists of a large
body of area A; its temperature is maintained at T₂ because it radiates
energy into space as much heat as is delivered to it by the engine.
The rate of this radiation is σAT2 where σ is a constant. The Carnot
engine has to be designed so that, for a given Wand T₁, A has a minimum
value. Show that A has a minimum value when T₂ takes the value 3T₁/4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F698145ac-df3f-4563-a82f-ea5332c53d66%2F6b276169-4de4-47b2-bc4e-9ec43e14cffc%2Fxizxbkn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A Carnot engine working on a satellite in outer space has to deliver a
fixed amount of power at rate W. The temperature of the heat source is
also fixed, at T₁. The lower temperature reservoir at T2 consists of a large
body of area A; its temperature is maintained at T₂ because it radiates
energy into space as much heat as is delivered to it by the engine.
The rate of this radiation is σAT2 where σ is a constant. The Carnot
engine has to be designed so that, for a given Wand T₁, A has a minimum
value. Show that A has a minimum value when T₂ takes the value 3T₁/4.
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