BITSAT2018PhysicsThermodynamicsActual
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?
Options
- A2 . 7 × 10 5   cal ,   70 . 70   %
- B7 . 27 × 10 5   cal ,   72 . 72   %
- C2 . 70 × 10 5   cal ,   80 . 70   %
- D3 . 70 × 10 5   cal ,   70 . 70   %
Correct answer
B. 7 . 27 × 10 5   cal ,   72 . 72   %
Step-by-step solution
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   %