Question

A certain coal-fired power plant has a rated power capacity of P = 550 MW. The output of this plant is W = 0.27QH, where QH is the energy input as heat from the hot reservoir. show answer No Attempt 14% Part

(a) Write an equation for the efficiency of a heat engine in terms of QH and the heat QC exhausted to a low temperature reservoir.
(b) Which would increase the efficiency more, doubling QH or reducing QC by half? No Attempt No Attempt 14% Part
(c) Calculate the maximum thermal efficiency of the power plant. No Attempt No Attempt 14% Part
(d) Calculate the absolute value of the exhausted heat (QC) each second in MJ for the power plant. No Attempt No Attempt 14% Part
(e) If the power plant operates for a full day at its rated capacity, how much energy QH in MJ is needed? No Attempt No Attempt 14% Part
(f) If, on average, one ton of coal contains Q = 25 GJ of energy, how many tons nH of coal would the plant need to operate for a day at its rated capacity? No Attempt No Attempt 14%
(g) How many tons nC of this coal is exhausted as wasted heat to QC in a single day?

Answer 1

This detailed answer addresses various questions related to a coal-fired power plant, including the efficiency of a heat engine, the effect of doubling QH versus reducing QC by half, calculating the maximum thermal efficiency, the exhausted heat each second, the energy needed for a full day of operation, the number of tons of coal needed, and the amount of coal exhausted as wasted heat in a single day.

Step-by-step explanation:

(a) The efficiency of a heat engine can be expressed as the ratio of the work output to the heat input. In this case, the equation for the efficiency is:

Efficiency = (Work Output / Heat Input) = W / QH

(b) To determine which would increase the efficiency more, we need to compare the effect of doubling QH versus reducing QC by half. Let's assume W1 and W2 represent the efficiencies before and after the change respectively:

W1 = 0.27QH and W2 = 0.27(2QH) = 0.54QH

The increase in efficiency can be calculated as:

Percentage Increase = ((W2 - W1) / W1) x 100

(c) To calculate the maximum thermal efficiency of the power plant, we need to find the value of QH that maximizes the efficiency. Unfortunately, the given information does not provide enough details to determine this value.

(d) The exhausted heat (QC) each second can be calculated using the equation QC = QH - W. Since W = 0.27QH, we can substitute this value to get:

QC = QH - 0.27QH = 0.73QH

(e) If the power plant operates for a full day at its rated capacity, the energy QH needed can be calculated by multiplying the rated power capacity by the number of seconds in a day:

QH = P x (24 hours x 60 minutes x 60 seconds)

(f) To determine the number of tons of coal needed to operate the plant for a day at its rated capacity, we need to calculate the energy content of one ton of coal and divide the total energy required by that value:

nH = (QH / Q)

(g) To calculate the amount of coal exhausted as wasted heat to QC in a single day, we can divide the exhausted heat (QC) by the energy content of one ton of coal:

nC = (QC / Q)