Question

11.35 An electric power plant uses energy from burning coal to generate steam at 450 Degrees Celsius. The plant is cooled by 20 Degrees Celsius water from a nearby river. If burning coal provides 100 MJ of heat, what is the theoretical minimum amount of heat that must be transferred to the river during the conversion of heat to electric energy?

A. 100 MJ
B. 90 MJ
C. 60 MJ
D. 40 MJ

Answer 1

The theoretical minimum amount of heat that must be transferred to the river when converting heat to electric energy in a coal-fired power plant is 58% of the input heat, which equates to 58 MJ; therefore, the closest answer is 60 MJ.

Step-by-step explanation:

The student is asking about the theoretical minimum amount of heat that must be transferred to the river while converting heat to electric energy in a coal-fired power plant that is cooled by 20 Degrees Celsius water. Using the Second Law of Thermodynamics and knowing that typical efficiency for such power plants is approximately 42%, we can deduce that the remaining energy that is not converted to work, which corresponds to 100% - 42% = 58%, must be transferred as heat to the surroundings. Thus, if the power plant receives 100 MJ of heat from burning coal, the theoretical minimum amount of heat transferred to the river would be 0.58 x 100 MJ = 58 MJ. The closest answer to this theoretical minimum is Option C: 60 MJ, taking into account that actual values might slightly differ due to real-world inefficiencies not captured in this idealized calculation.