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?

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

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards