Question

a heat engine absorbs heat at a temperature of 900 k, turns some of it to electrical power, and rejects the remainder at 600 k. a second heat engine absorbs all the heat rejected by the first heat engine, turns some of it to electrical power, and rejects the remainder at 300 k. suppose each engine is operating at its maximum possible thermodynamic efficiency. if the first heat engine is absorbing 1 kw of heat, what electrical power output is the second heat engine producing?

Answer 1

The electrical power output of the second heat engine is 0.3335 kW or 333.5 Watts, assuming each engine operates at maximum thermodynamic efficiency.

Step-by-step explanation:

The question involves finding the electrical power output of the second heat engine in a sequential process where the first heat engine operates between 900 K and 600 K and the second engine uses the rejected heat from the first engine to operate between 600 K and 300 K.

Using the Carnot efficiency formula, which is η = 1 - (Tc/Th), where η is the efficiency, Tc is the cold reservoir temperature, and Th is the hot reservoir temperature, we can calculate the efficiency of both engines.

For the first engine:

• Th1 = 900 K
• Tc1 = 600 K
• η_1 = 1 - (Tc1/Th1) = 1 - (600/900) = 0.333 (or 33.3%)

The heat rejected by the first engine acting as the input for the second engine is: Q_rejected = (1 - η_1) * Q_absorbed = (1 - 0.333) * 1 kW = 0.667 kW

For the second engine:

• Th2 = 600 K
• Tc2 = 300 K
• η_2 = 1 - (Tc2/Th2) = 1 - (300/600) = 0.5 (or 50%)

The power output of the second engine will be:

P_output = η_2 * Q_rejected = 0.5 * 0.667 kW = 0.3335 kW