Question

Assume that the turbines at a coal-powered power plant were upgraded, resulting in an improvement in efficiency of 3.32%. Assume that prior to the upgrade the power station had an efficiency of 36% and that the heat transfer into the engine in one day is still the same at 2.50×10¹⁴ J. (a) How much more electrical energy is produced due to the upgrade? (b) How much less heat transfer occurs to the environment due to the upgrade?

a) 6.00×10¹² J, 4.00×10¹² J
b) 6.50×10¹² J, 4.25×10¹² J
c) 7.00×10¹² J, 4.50×10¹² J
d) 7.50×10¹² J, 4.75×10¹² J

Answer 1

The additional electrical energy produced due to the upgrade is 8.3x10¹² J, and the reduction in heat transfer to the environment is also 8.3x10¹² J.

Step-by-step explanation:

To calculate the additional electrical energy produced due to the turbine upgrade, we need to find the difference in efficiency before and after the upgrade. The improvement in efficiency is 3.32%, so the new efficiency is 36% + 3.32% = 39.32%. The additional electrical energy produced is the difference between the work output before and after the upgrade.

Using the formula: Additional electrical energy = (New efficiency - Old efficiency) × Heat transfer into the engine.

Substituting the values:

Additional electrical energy = (39.32% - 36%) × 2.50x10¹⁴ J = 0.0332 × 2.50x10¹⁴ J = 8.3x10¹² J.

Therefore, the answer to (a) is 8.3x10¹² J.

To calculate the reduction in heat transfer to the environment due to the upgrade, we can use the same formula:

Reduction in heat transfer = (Old efficiency - New efficiency) × Heat transfer into the engine.

Substituting the values: Reduction in heat transfer = (36% - 39.32%) × 2.50x10¹⁴ J = -0.0332 × 2.50x10¹⁴ J = -8.3x10¹² J.

Since heat transfer cannot be negative, we take the absolute value, so the reduction in heat transfer is 8.3x10¹² J.

Therefore, the answer to (b) is 8.3x10¹² J.