A reservoir is at 827 ° C and Carnot's engine takes a thousand kilo calorie of heat from it and exhausts it to a sink at 27 ° C . What is the amount of work and the efficiency of the engine?

Question

A reservoir is at 827 ° C and Carnot's engine takes a thousand kilo calorie of heat from it and exhausts it to a sink at 27 ° C . What is the amount of work and the efficiency of the engine?, 2 . 7 × 10 5 cal , 70 . 70 %, 7 . 27 × 10 5 cal , 72 . 72 %, 2 . 70 × 10 5 cal , 80 . 70 %, 3 . 70 × 10 5 cal , 70 . 70 %

MARKS App · Accepted Answer

Given, Q 1 = 10 6 cal T 1 = 827 ° C = ( 827 + 273 ) = 1100 K , T 2 = 27 ° C = ( 27 + 273 ) = 300 K . As, Q 1 T 1 = Q 2 T 2 ∴ Q 2 = T 2 T 1 Q 1 = 300 1100 × 10 6 = 2 . 72 × 10 5 cal work done, W = Q 1 - Q 2 = 10 6 - 2 . 72 × 10 5 = 7 . 27 × 10 5 cal The efficiency of the engine, η = 1 - T 2 T 1 × 100 ⇒ η = 1 - 300 1100 × 100 = 72 . 72 %

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