The following heat engine produces power of 100,000 kW. The heat engin...
Power produced by engine = Workdone(W) = 100,000 k
= 50% of Carnot cycle or engine
Also,
= 320 MW
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The following heat engine produces power of 100,000 kW. The heat engin...
Given data:
- Power output of the heat engine = 100,000 kW
- Temperature of the hot reservoir (Th) = 800 K
- Temperature of the cold reservoir (Tc) = 300 K
- Thermal efficiency of the heat engine = 50% of the Carnot engine efficiency for the same temperatures
Approach:
To find the rate at which heat is absorbed from the hot reservoir, we need to determine the thermal efficiency of the Carnot engine first.
Then, we can use the formula for thermal efficiency to calculate the rate of heat absorption.
Calculation:
1. Carnot engine efficiency:
The Carnot engine efficiency is given by the formula:
ηCarnot = 1 - Tc/Th
Substituting the given values,
ηCarnot = 1 - (300/800) = 0.625
2. Heat engine efficiency:
The thermal efficiency of the heat engine is given as 50% of the Carnot engine efficiency.
ηHeat Engine = 0.5 * ηCarnot = 0.5 * 0.625 = 0.3125
3. Calculation of heat absorbed:
The thermal efficiency of a heat engine is given by the formula:
η = (Qh - Qc) / Qh
where Qh is the heat absorbed from the hot reservoir and Qc is the heat rejected to the cold reservoir.
Rearranging the formula, we get:
Qh = Qc / (1 - η)
Since the power output of the heat engine is given as 100,000 kW, we can calculate the heat rejected as:
Qc = Power output / Efficiency = 100,000 kW / 0.3125 = 320,000 kW
Substituting the values into the formula, we can calculate the heat absorbed:
Qh = 320,000 kW / (1 - 0.3125) = 320,000 kW / 0.6875 = 465,454.55 kW
Converting the heat absorbed into MW:
Qh = 465,454.55 kW / 1,000 = 465.45455 MW
Therefore, the rate at which heat is absorbed from the hot reservoir is approximately 465.45455 MW.
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