Question

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?

Answer 1

Answer:

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