A Carnot engine is operated between two heat reservoirs at temperatures of 550 K and 300 K. 1.) If the engine receives 6.70 kJ of heat energy from the reservoir at 550 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K? 2.) How much mechanical work is performed by the engine during each cycle?

Question

Physics

Eden Black

13 September, 16:57

A Carnot engine is operated between two heat reservoirs at temperatures of 550 K and 300 K. 1.) If the engine receives 6.70 kJ of heat energy from the reservoir at 550 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K? 2.) How much mechanical work is performed by the engine during each cycle?

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Answers (1)

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Janelle Cain · Answer 1

a) 3654.5 joules per cycle is rejected to the reservoir at 300 K by the Carnot Engine.

b) Mechanical work performed by the engine during each cycle = 3045.5 J = 3.046 KJ

Explanation:

For a Carmot engine,

(Q꜀/T꜀) + (Qₕ/Tₕ) = 0

(Q꜀/T꜀) = - (Qₕ/Tₕ)

Q꜀ = - T꜀ * (Qₕ/Tₕ)

Qₕ = 6.70 KJ

Tₕ = 550 K

Q꜀ = ?

T꜀ = 300 K

Q꜀ = - 300 (6700/550) = - 3654.5 J = - 3.65 KJ

b) Mechanical work done by the Carnot engine is given by

W = |Qₕ| - |Q꜀| = 6700 - 3654.5 = 3045.5 J