Final answer:
The power output of the coal power plant is approximately 1041.67 MW, calculated using the given efficiency and the heat of combustion of coal by finding the total energy produced and then converting the useful energy to power.
Step-by-step explanation:
The student asked about the power output of a coal power plant with a known efficiency that burns a specific amount of coal per day. The heat of combustion for coal is given as 30MJ/kg.
To calculate the power output, we need to perform a few steps:
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Step 1: Total energy from coal = mass of coal × heat of combustion = 10 million kg × 30MJ/kg = 300×10⁶ MJ.
Step 2: Useful energy (electrical) = Total energy produced × Efficiency = 300⁶ MJ × 0.3 = 90×10⁶ MJ.
Step 3: Power output = Useful energy / time (in seconds) = (90×10⁶ MJ) / (24 hours × 3600 seconds) = (90×10⁶ × 10⁶ J) / (86400 s) ≈ 1041.67 MW.
Therefore, the power output of the plant is approximately 1041.67 MW.