Final answer:
To find the additional electrical energy produced from an efficiency upgrade and the reduced heat transfer to the environment, we calculate the energy outputs before and after the improvement and then determine the differences in electrical energy and residual heat.
Step-by-step explanation:
When turbines at a coal-powered power plant were upgraded, resulting in an improvement in efficiency of 3.32%, the power station went from an efficiency of 36% to 39.32%. Given that the heat transfer into the engine remains constant at 2.50×10¹⁴ J over one day, we can calculate the additional electrical energy produced and the reduced heat transfer to the environment.
(a) The initial electrical energy output at 36% efficiency is E1 = 0.36 × 2.50×10¹⁴ J. The upgraded electrical energy output at 39.32% efficiency is E2 = 0.3932 × 2.50×10¹⁴ J. The difference, ΔE = E2 - E1, represents the additional electrical energy produced due to the upgrade.
(b) The reduction in heat transfer to the environment can be found by subtracting the upgraded electrical energy output from the initial heat transfer, and comparing it to the initial residual heat transfer to the environment. The initial heat transfer to the environment is H1 = (1 - 0.36) × 2.50×10¹⁴ J, and the upgraded heat transfer to the environment is H2 = (1 - 0.3932) × 2.50×10¹⁴ J. The heat transfer reduction is ΔH = H1 - H2.