Question:

A heat engine operates between two reservoirs at temperatures T₁ = 600 K and T₂ = 300 K. The engine absorbs 1000 J of heat from the hot reservoir during each cycle and delivers 550 J of work output during the same cycle. Calculate the entropy change of the engine for each cycle.

Answer:

To calculate the entropy change of the engine for each cycle, we need to apply the entropy change equation for a heat engine:

ΔS = Q_h / T_h - Q_c / T_c

where ΔS is the entropy change, Q_h is the heat absorbed from the hot reservoir, T_h is the temperature of the hot reservoir, Q_c is the heat rejected to the cold reservoir, and T_c is the temperature of the cold reservoir.

In this case, we are given Q_h = 1000 J, T_h = 600 K, and Q_c = -550 J (since work delivered is negative), and T_c = 300 K.

Plugging the given values into the entropy change equation, we get:

ΔS = (1000 J) / (600 K) - (-550 J) / (300 K)

Simplifying the equation further:

ΔS = 1.67 J/K + 1.83 J/K

ΔS = 3.5 J/K

Therefore, the entropy change of the engine for each cycle is 3.5 J/K.

Note: The negative sign in the equation for Q_c is due to the fact that the heat rejected to the cold reservoir is considered negative conventionally.