Final answer:
The upgraded turbines led to an increase in electrical energy output by roughly 0.83x10¹ J. Concurrently, there was a decrease in heat transfer to the environment amounting to about 0.03x10¹⁴ J or 3.00x10¹⁰ J.
Step-by-step explanation:
When turbines at a coal-powered power plant are upgraded and become more efficient, this impacts both the amount of electrical energy the plant produces and the heat transfer to the environment. Let's calculate these changes given an efficiency upgrade.
Calculating Increased Electrical Energy Output
The original efficiency of the power station was 36%, and after upgrade, it improved by 3.32%, making it 39.32%. To find out how much additional electrical energy is produced due to the upgrade:
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- Calculate the total energy output before the upgrade:
0.36 × 2.50×10¹⁴ J = 9.00×10¹ J.
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- Calculate the total energy output after the upgrade:
0.3932 × 2.50×10¹⁴ J = 9.83×10¹ J.
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- The increase in energy output is the difference between the two:
9.83×10¹ J - 9.00×10¹ J = 0.83×10¹ J.
Calculating Reduced Heat Transfer to the Environment
To find out how much less heat transfer occurs to the environment due to the upgrade:
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- Before the upgrade, the waste heat is the remaining part after energy conversion:
2.50×10¹⁴ J - 9.00×10¹ J = 1.61×10¹⁴ J.
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- After the upgrade, the waste heat is:
2.50×10¹⁴ J - 9.83×10¹ J = 1.58×10¹⁴ J.
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- The reduction in heat transfer to the environment is the difference between the two:
1.61×10¹⁴ J - 1.58×10¹⁴ J = 0.03×10¹⁴ J or 3.00×10¹⁰ J.